Tootfinder

There may be an $n$-entangled set but no $n 1$-entangled sets
Jorge Antonio Cruz Chapital
https://arxiv.org/abs/2509.01029 https://arxiv.org/pdf/2509.01029…

There may be an $n$-entangled set but no $n+1$-entangled sets
In this paper we show that for every $2\leq n\in \mathbb{N}$, the statement "there is an $n$-entangled set, but there are no $n+1$-entangled sets" is consistent. We also prove some theorems which improve our understanding of entangled sets in relation to construction schemes: (1) The axiom FCA$^Δ$ introduced in \cite{finitizationclubch} implies the existence of $n$-entangled sets which are not $n+1$-entangled. (2) $\mathfrak{m}_\mathcal{F}>ω_1$ implies the non-existence of entangled sets. Thu…

Further Applications of Cubic $q$-Binomial Transformations
Alexander Berkovich, Aritram Dhar
https://arxiv.org/abs/2510.00130 https://arxiv.org/pdf/2510.00…

Further Applications of Cubic $q$-Binomial Transformations
Consider \begin{align*} G(N,M;α,β,K,q) = \sum\limits_{j\in\mathbb{Z}}(-1)^jq^{\frac{1}{2}Kj((α+β)j+α-β)}\left[\begin{matrix}M+N\\N-Kj\end{matrix}\right]_{q}. \end{align*} In this paper, we prove the non-negativity of coefficients of some cases of $G(N,M;α,β,K,q)$. For instance, for non-negative integers $n$ and $t$, we prove that \begin{align*} G\left(n,n;\frac{4}{3}+\frac{3(3^t-1)}{2},\frac{5}{3}+\frac{3(3^t-1)}{2},3^{t+1},q\right) \end{align*} and \begin{align*} G\left(n-\frac{3^t-1}{…

Degree sequences realizing labelled perfect matchings
Joseph Briggs, Jessica McDonald, Songling Shan
https://arxiv.org/abs/2510.01110 https://arxiv.org/pdf…

Degree sequences realizing labelled perfect matchings
Let $n\in \mathbb{N}$ and $d_1 \geq d_2 \geq d_n\geq 1$ be integers. There is characterization of when $(d_1, d_1, \ldots, d_n)$ is the degree sequence of a graph containing a perfect matching, due to results of Lovász (1974) and Erdős and Gallai (1960). But \emph{which} perfect matchings can be realized in the labelled graph? Here we find the extremal answers to this question, showing that the sequence $(d_1, d_2, \ldots, d_n)$: (1) can realize a perfect matching iff it can realize $\{(1, n)…

On the Fermat-type partial differential-difference equations on $\mathbb{C}^n$
Tingbin Cao, Jun Wang, Zhuan Ye
https://arxiv.org/abs/2509.01862 https://arx…

On the Fermat-type partial differential-difference equations on $\mathbb{C}^n$
Assume that $n$ is a positive integer, $p_{j}$ ($j=1,2, \cdots, 6)$ are polynomials, $p$ is an irreducible polynomial, and $f$ is an entire function on $\mathbb{C}^{n}.$ Let $ L(f)=\sum_{j=1}^s q_{t_j}f_{z_{t_j}}$ and $\overline{f}(z)=f(z_{1}+c_{1}, \ldots, z_{n}+c_{n})$, where $q_{t_j}$ ($j=1,2, \cdots, s\le n$) are non-zero polynomials on $\mathbb{C}^{n}$ and $c=(c_{1}, \ldots, c_{n})\in \mathbb{C}^{n}\setminus\{0\}$. We show the structures of all entire solutions to the non-linear partial di…

“Danny Danon, the Israeli ambassador to the U.N. … disparaged Albanese personally, calling her a ‘witch.’”
https://apnews.com/article/united-nations-israel-gaza-human-rights-albanese-e1a4fbde166e34bc8d305bfbf6e2bd51

UN investigator delivers Gaza report virtually due to US sanctions
An independent U.N. investigator is taking world nations to task for not standing up to the U.S. over sanctions it imposed on her. The sanctions prompted the expert to give a report to the U.N. by video on Tuesday. Francesca Albanese is an Italian human rights lawyer assigned to explore human rights abuses in the Palestinian territories. She told the U.N. General Assembly by video that the U.S. sanctions are “spiteful” and attack the world body's independence and integrity. The U.S. has acc…

Partition functions of two-dimensional Coulomb gases with circular root- and jump-type singularities
Kohei Noda
https://arxiv.org/abs/2510.00843 https://ar…

Partition functions of two-dimensional Coulomb gases with circular root- and jump-type singularities
In this paper, we study the random polynomial $p_n(ρ):=\prod_{j=1}^n (|z_j|-ρ)$, where the points $\{z_j\}_{j=1}^n$ are the eigenvalue moduli of random normal matrices with a radially symmetric potential. We establish precise large $n$ asymptotic expansions for the moment generating function \[ \mathbb{E}\!\left[e^{\tfrac{u}π\mathrm{Im}\log p_n(ρ)}\, e^{a\,\mathrm{Re}\log p_n(ρ)}\right], \qquad u\in\mathbb{R}, \; a>-1, \] where $ρ>0$ lies in the bulk of the spectral droplet. The…

Low regularity Sobolev well-posedness for Vlasov--Poisson
In-Jee Jeong, Sangwook Tae
https://arxiv.org/abs/2510.02112 https://arxiv.org/pdf/2510.02112

Low regularity Sobolev well-posedness for Vlasov--Poisson
We consider the Vlasov--Poisson equation on $\mathbb{R}^n \times \mathbb{R}^n$ with $n \ge 3$. We prove local well-posedness in $H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ with $s> n/2-1/4$, for initial distribution $f_{0} \in H^{s}(\mathbb{R}^n \times \mathbb{R}^n)$ having compact support in $v$. In particular, data not belonging to $L^p(\mathbb{R}^n \times \mathbb{R}^n)$ for large $p$ are allowed.

Sequences of surfaces in $4$-manifolds
Marina Ville
https://arxiv.org/abs/2509.00566 https://arxiv.org/pdf/2509.00566…

Sequences of surfaces in $4$-manifolds
Let $(Σ_n)$ be a sequence of surfaces immersed in a $4$-manifold $M$ which converges to a branched surface $Σ_0$ .\\ We denote by $k^T_p$ (resp. $k^N_p$) the amount of curvature of the tangent bundles $TΣ_n$ (resp. normal bundles $NΣ_n$) which concentrates around a branch point $p$ of $Σ_0$ when $n$ goes to infinity. Alternatively $k^T\pm k^N$ measures how much the twistor degrees drop when we go from $Σ_n$ to $Σ_0$. For complex algebraic curves, $k^T+k^N=0$..\\ In some instances - 1) if…

A viscosity solution approach to the large deviation principle for stochastic convective Brinkman-Forchheimer equations
Sagar Gautam, Manil T. Mohan
https://arxiv.org/abs/2510.01166

A viscosity solution approach to the large deviation principle for stochastic convective Brinkman-Forchheimer equations
This article develops the viscosity solution approach to the large deviation principle for the following two- and three-dimensional stochastic convective Brinkman-Forchheimer equations on the torus $\mathbb{T}^d,\ d\in\{2,3\}$ with small noise intensity: \begin{align*} \mathrm{d}\boldsymbol{u}_n+[-μΔ\boldsymbol{u}_n+ (\boldsymbol{u}_n\cdot\nabla)\boldsymbol{u}_n +α\boldsymbol{u}_n+β|\boldsymbol{u}_n|^{r-1}\boldsymbol{u}_n+\nabla p_n]\mathrm{d} t=\boldsymbol{f}\mathrm{d} t+\fra…

Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces
S\'andor Kisfaludi-Bak, Geert van Wordragen
https://arxiv.org/abs/2509.01443 https://

Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces
We consider Steiner spanners in Euclidean and non-Euclidean geometries. In the Euclidean setting, a recent line of work initiated by Le and Solomon [FOCS'19] and further improved by Chang et al. [SoCG'24] obtained Steiner $(1+\varepsilon)$-spanners of size $O_d(\varepsilon^{(1-d)/2}\log(1/\varepsilon)n)$, nearly matching the lower bounds of Bhore and Tóth [SIDMA'22]. We obtain Steiner $(1+\varepsilon)$-spanners of size $O_d(\varepsilon^{(1-d)/2}\log(1/\varepsilon)n)$ not only in $d$-dimensio…

Short-time blowup statistics of a Brownian particle in repulsive potentials
Baruch Meerson
https://arxiv.org/abs/2509.01252 https://arxiv.org/pdf/2509.0125…

Short-time blowup statistics of a Brownian particle in repulsive potentials
We study the dynamics of an overdamped Brownian particle in a repulsive scale-invariant potential $V(x) \sim -x^{n+1}$. For $n > 1$, a particle starting at position $x$ reaches infinity in a finite, randomly distributed time. We focus on the short-time tail $T \to 0$ of the probability distribution $P(T, x, n)$ of the blowup time $T$ for integer $n > 1$. Krapivsky and Meerson [Phys. Rev. E \textbf{112}, 024128 (2025)] recently evaluated the leading-order asymptotics of this tail, which exhibits…

Clique number of xor-powers of Kneser graphs
Zolt\'an F\"uredi, Andr\'as Imolay, \'Ad\'am Schweitzer
https://arxiv.org/abs/2510.01509 https://

Clique number of xor-powers of Kneser graphs
Let $f_\ell(n, k)$ denote the clique number of the xor-product of $\ell$ isomorphic Kneser graphs KG(n,k). Alon and Lubetzky investigated the case of complete graphs as a coding theory problem and showed $f_\ell(n,1)\leq \ell n +1$. Imolay, Kocsis, and Schweitzer proved that $f_2(n,k)\leq n/k +c(k)$. Here, the order of magnitude of $c(k)$ is determined to be $Θ\left( k \binom{2k}{k} \right)$. By explicit constructions and by an algebraic proof, it is shown that $\ell n- 2\ell-1 \leq f_\ell(n…

Kennedy Fires N.I.H. Scientist Who Filed Whistle-Blower Complaint (Benjamin Mueller/New York Times)
https://www.nytimes.com/2025/10/02/health/kennedy-marrazzo-nih.html?unlocked_article_code=1.qU8.CZUc.qtTuKldwzHgT&smid=nytcore-ios-share&referringSource=articleShare
http://www.memeorandum.com/251003/p3#a251003p3

The Bruhat-Tits stratification for basic unramified $GU(1,n-1)$ Rapoport-Zink spaces at arbitrary parahoric level
Joseph Muller
https://arxiv.org/abs/2510.00580 https://

The Bruhat-Tits stratification for basic unramified $GU(1,n-1)$ Rapoport-Zink spaces at arbitrary parahoric level
In this paper, we describe a stratification on the reduced special fiber of the basic unramified unitary Rapoport-Zink space of signature $(1,n-1)$ and at arbitrary parahoric level. We prove the smoothness, irreducibility and compute the dimensions of the closed strata, which are isomorphic to the closure of certain fine Deligne-Lusztig varieties for a product of unitary and general linear groups. We also describe the incidence relations of the stratification by using Bruhat-Tits indices, which…

Amazon plans to end the ability for Prime members to share free shipping benefits with individuals outside their household, starting on October 1 (Emma Roth/The Verge)
https://www.theverge.com/news/769051/amazon-prime-free-shipping-benefit-sharing-endin…

Amazon ends shared Prime free shipping outside your home
Amazon is ending the program that lets Prime members share their free shipping perk with people who don’t live with them. The change goes into effect on October 1st, 2025.

Hot-Ion Modes in Globus-M2 and Saturation of Energy Confinement Time Scaling in Spherical Tokamaks with Toroidal Magnetic Field of 1 T and Above
G. S. Kurskiev, V. B. Minaev, N. V. Sakharov, V. K. Gusev, Yu. V. Petrov, I. V. Miroshnikov, F. V. Chernyshev, N. N. Bakharev, E. O. Kiselev, A. Yu. Telnova, E. E. Tkachenko, N. S. Zhiltsov, Globus- M2 Team
https://

Hot-Ion Modes in Globus-M2 and Saturation of Energy Confinement Time Scaling in Spherical Tokamaks with Toroidal Magnetic Field of 1 T and Above
In a small spherical tokamak with minor radius of 0.22 m and toroidal magnetic field of 1 T, it is possible to heat ions of a sufficiently dense plasma to an extremely high temperature up to 50 million Kelvin. To do this, it is necessary to transfer a sufficiently large torque to stabilize ion-scale turbulence and achieve ion heat transport at neoclassical level reaching extremely low values of plasma collisionality. It is also necessary to ensure good thermal insulation of electrons, which is …

Binomial edge ideals of Cameron-Walker graphs
Takayuki Hibi, Sara Saeedi Madani
https://arxiv.org/abs/2509.01150 https://arxiv.org/pdf/2509.01150

Binomial edge ideals of Cameron-Walker graphs
Let $G$ be a Cameron--Walker graph on $n$ vertices and $J_G$ the binomial edge ideal of $G$. Let $S$ denote the polynomial ring in $2n$ variables over a field. It is shown that the following conditions are equivalent: (i) $S/J_G$ is Cohen--Macaulay; (ii) $J_G$ is unmixed; (iii) $\dim (S/J_G) = n+1$; (iv) (a) $n = 3$ and $G$ is a path of length $2$ or (b) $n = 5$ and $G$ is a path of length $4$ or (c) $n=5$ and $G$ is obtained by attaching a path of length $2$ to a triangle. Moreover, the depth …

Homogeneous fractional integral operators on weighted Lebesgue, Morrey and Campanato spaces
Jingliang Du, Hua Wang
https://arxiv.org/abs/2510.00426 https://

Homogeneous fractional integral operators on weighted Lebesgue, Morrey and Campanato spaces
Let $0<α

Quantum Phase Sensitivity with Generalized Coherent States Based on Deformed su(1,1) and Heisenberg Algebras
N. E. Abouelkhir, A. Slaoui, R. Ahl Laamara
https://arxiv.org/abs/2508.21779

Quantum Phase Sensitivity with Generalized Coherent States Based on Deformed su(1,1) and Heisenberg Algebras
We investigate the phase sensitivity of a Mach Zehnder interferometer using a special class of generalized coherent states constructed from generalized Heisenberg and deformed su(1,1) algebras. These states, derived from a perturbed harmonic oscillator with a four parameter deformed spectrum, provide enhanced tunability and nonclassical features. The quantum Fisher information and its associated quantum Cramér-Rao bound are used to define the fundamental precision limits in phase estimation. W…

Constructive l2-Discrepancy Minimization with Additive Deviations
Kunal Dutta
https://arxiv.org/abs/2508.21423 https://arxiv.org/pdf/2508.21423

Constructive l2-Discrepancy Minimization with Additive Deviations
The \emph{signed series} problem in the $\ell_2$ norm asks, given set of vectors $v_1,\ldots,v_n\in \mathbf{R}^d$ having at most unit $\ell_2$ norm, does there always exist a series $(\varepsilon_i)_{i\in [n]}$ of $\pm 1$ signs such that for all $i\in [n]$, $\max_{i\in [n]} \|\sum_{j=1}^i \varepsilon_i v_i\|_2 = O(\sqrt{d})$. A result of Banaszczyk [2012, \emph{Rand. Struct. Alg.}] states that there exist signs $\varepsilon_i\in \{-1,1\},\; i\in [n]$ such that $\max_{i\in [n]} \|…

Generalized Parallel Scaling with Interdependent Generations
Harry Dong, David Brandfonbrener, Eryk Helenowski, Yun He, Mrinal Kumar, Han Fang, Yuejie Chi, Karthik Abinav Sankararaman
https://arxiv.org/abs/2510.01143

Generalized Parallel Scaling with Interdependent Generations
Parallel LLM inference scaling involves sampling a set of $N>1$ responses for a single input prompt. However, these $N$ parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent resp…

Infinitely presented simple groups separated by homological finiteness properties
Claudio Llosa Isenrich, Eduard Schesler, Xiaolei Wu
https://arxiv.org/abs/2510.01952 https://…

Infinitely presented simple groups separated by homological finiteness properties
Given a finitely generated linear group $G$ over $\mathbb{Q}$, we construct a simple group $Γ$ that has the same finiteness properties as $G$ and admits $G$ as a quasi-retract. As an application, we construct a simple group of type $\mathrm{FP}_{\infty}$ that is not finitely presented. Moreover we show that for every $n \in \mathbb{N}$ there is a simple group of type $\mathrm{FP}_n$ that is neither finitely presented nor of type $\mathrm{FP}_{n+1}$. Since our simple groups arise as Röver--Nek…

A symmetric biderivation structure on polynomial algebras and a class of modules over the special Jordan algebra $H_n(K)$ of symmetric matrices
Yangjie Yin, Gang Han
https://arxiv.org/abs/2509.25867

A symmetric biderivation structure on polynomial algebras and a class of modules over the special Jordan algebra $H_n(K)$ of symmetric matrices
There exists a biderivation structure on the polynomial algebra $\mathscr{A}[n] = K[x_1,\dots,x_n],$ where $K$ is a field with $\operatorname{char}(K)\ne 2$, defined by $f \circ h = \sum_{i=1}^n \frac{\partial f}{\partial x_i}\,\frac{\partial h}{\partial x_i}.$ Let $\mathscr{A}_k[n]$ denote the subspace of homogeneous polynomials of degree $k$. Then $(\mathscr{A}_2[n],\circ)$ is a Jordan algebra, isomorphic to the special Jordan algebra $H_n(K)$ of $n\times n$ symmetric matrices. Each $\mathscr…

Measurement of Dark Matter Substructure from the Kinematics of the GD-1 Stellar Stream
Jacob Nibauer, Ana Bonaca, Adrian M. Price-Whelan, David N. Spergel, Jenny E. Greene
https://arxiv.org/abs/2510.02247

Measurement of Dark Matter Substructure from the Kinematics of the GD-1 Stellar Stream
Stellar streams are sensitive tracers of low-mass dark matter subhalos and provide a means to test the Cold Dark Matter (CDM) paradigm on small scales. In this work, we connect the intrinsic velocity dispersion of the GD-1 stream to the number density and internal structure of dark matter subhalos in the mass range $10^5$-$10^9\ M_\odot$. We measure the radial velocity dispersion of GD-1 based on 160 identified member stars across four different spectroscopic catalogs. We use repeat observation…

[C/N] Ages for Red Giants and their Implications for Galactic Archaeology
John D. Roberts, Marc H. Pinsonneault, Jennifer A. Johnson, Liam O. Dubay, James W. Johnson
https://arxiv.org/abs/2509.25321

[C/N] Ages for Red Giants and their Implications for Galactic Archaeology
Red giants undergo the first dredge-up, a mixing event that creates a connection between their surface [C/N] and their mass and age. We derive a [C/N]-Age relationship for red giants calibrated on APOGEE DR17 abundances and APOKASC-3 asteroseismic ages. We find that we can use [C/N] to reliably recover asteroseismic ages between 1 and 10 Gyr with average uncertainties of 1.64 Gyr. We find that [C/N] yields concordant ages, with modest offsets, for stars in different evolutionary states. We also…

Hook immanantal inequalities for totally nonnegative matrices
Mark Skandera
https://arxiv.org/abs/2510.00327 https://arxiv.org/pdf/2510.00327

Hook immanantal inequalities for totally nonnegative matrices
Given a weakly decreasing positive integer sequence $λ= (λ_1,\dotsc,λ_\ell)$ summing to $n$, let $χ^λ$ denote the irreducible character of the symmetric group $S_n$ indexed by $λ$. This representation has dimension $χ^λ(e)$, where $e$ is the identity element of $S_n$. Let $\mathrm{Imm}_{χ^λ}$ denote the corresponding irreducible character immanant, the function on $n \times n$ matrices $A = (a_{i,j})$ defined by $\mathrm{Imm}_{χ^λ}(A) := \sum_{w \in S_n} χ^λ(w) a_{1,w_1} \cdots a_…

1/N Vastuullisuustyön hyödyn kai arvellaan lähinnä olevan siinä, että ollaan vastuullisia (!) ja siitä koituvat edut, mutta vastuullisuustekemisellä voi olla merkittäviä muita, välillisiä iloja ihan siksi, että se syventää asiaa työstävien ihmisten osaamista ja kasvattaa valmiuksia, luo intellektuaalista infraa. Tällaista voi tapahtua:

On the attaching map of the 3-cell skeleton of the homotopy fibre
Juxin Yang, Fengchun Lei, Jingyan Li, Jie Wu
https://arxiv.org/abs/2509.21444 https://arx…

On the attaching map of the 3-cell skeleton of the homotopy fibre
Localize spaces at 2. Let $f\inπ_{n+k}(S^{n})$, ($n\geq2$ and $k\geq0$) and let $F$ be the homotopy fibre of the pinch map $ΣC_{f}=S^{n+1}\cup e^{n+k+2} \rightarrow S^{n+k+2}$, (in the case $k=0$, further assume $ΣC_{f}\not\Simeq*$). As a type of Gray's relative James constructions, it is known that $ F$ has a CW decomposition $F=(S^{n+1}\cup_{\af} e^{2n+k+2})\cup_β e^{3n+2k+3}\cup \cdots$, where $\af=[1_{S^{n+1}},\s f]\inπ_{n+k+1}(S^{n})$ is the Whitehead product and $β$ is a higher Whit…

Yeah, Jimmy “I’m actually quite in favour of business and capitalism and all that”* Wales, the surveillance capitalist and Fandom-president adtech man who once told me he doesn’t believe in any form of government regulation – not even in food standards or healthcare – can go fuck himself.
Find better heroes. Or even better yet, get over the whole stupid concept itself.
*

Replaced article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Inertia groups of $(n-1)$-connected $2n$-manifolds
Andrew Senger, Adela YiYu Zhang

Crosslisted article(s) found for math.GN. https://arxiv.org/list/math.GN/new
[1/1]:
- There may be an $n$-entangled set but no $n 1$-entangled sets
Jorge Antonio Cruz Chapital

Bias Correction in Factor-Augmented Regression Models with Weak Factors
Peiyun Jiang, Yoshimasa Uematsu, Takashi Yamagata
https://arxiv.org/abs/2509.02066 https://

Bias Correction in Factor-Augmented Regression Models with Weak Factors
In this paper, we study the asymptotic bias of the factor-augmented regression estimator and its reduction, which is augmented by the $r$ factors extracted from a large number of $N$ variables with $T$ observations. In particular, we consider general weak latent factor models with $r$ signal eigenvalues that may diverge at different rates, $N^{α_{k}}$, $0<α_{k}\leq 1$, $k=1,\dots,r$. In the existing literature, the bias has been derived using an approximation for the estimated factors with a …

The sigma invariant of the $n$ torus, the K3 surface, and Euclidean and elliptic 3d manifolds
Santiago R. Simanca
https://arxiv.org/abs/2509.26079 https://…

The sigma invariant of the $n$ torus, the K3 surface, and Euclidean and elliptic 3d manifolds
On the space of isometric embeddings $f_g$ of metrics $g$ on a manifold $M^n$ into the standard $(\mb{S}^{\tn=\tn(n)},\tg)$, we consider the total exterior scalar curvature $Θ_{f_g}(M)$, and squared $L^2$ norm of the mean curvature vector $Φ_{f_g}(M)$ and second fundamental form $Π_{f_g}(M)$ functionals of $f_g$, respectively. Then $\mc{W}_{f_g}(M) =(1-δ_{n,1})(n/(n-1)) Θ_{f_{g}}(M) + Φ_{f_{g)}}(M)$ and $\mc{D}_{f_g}(M)=(1-δ_{n,1}) (1/(n-1))Θ_{f_g}(M)+Π_{f_{g)}}(M)$ are functionals int…

Large cliques and large independent sets: can they coexist?
Uriel Feige, Ilia Pauzner
https://arxiv.org/abs/2509.00721 https://arxiv.org/pdf/2509.00721

Large cliques and large independent sets: can they coexist?
For a graph $G$ and a parameter $k$, we call a vertex $k$-enabling if it belongs both to a clique of size $k$ and to an independent set of size $k$, and we call it $k$-excluding otherwise. Motivated by issues that arise in secret sharing schemes, we study the complexity of detecting vertices that are $k$-excluding. We show that for every $ε$, for sufficiently large $n$, if $k > (\frac{1}{4} + ε)n$, then every graph on $n$ vertices must have a $k$-excluding vertex, and moreover, such a vertex …

Constructions of Efficiently Implementable Boolean Functions with Provable Nonlinearity/Resiliency/Algebraic Immunity Trade-Offs
Palash Sarkar
https://arxiv.org/abs/2510.01720 h…

Constructions of Efficiently Implementable Boolean Functions with Provable Nonlinearity/Resiliency/Algebraic Immunity Trade-Offs
We describe several families of efficiently implementable Boolean functions achieving provable trade-offs between resiliency, nonlinearity, and algebraic immunity. In concrete terms, the following result holds for each of the function families that we propose. Given integers $m_0\geq 0$, $x_0\geq 1$, and $a_0\geq 1$, it is possible to construct an $n$-variable function which has resiliency at least $m_0$, linear bias (which is an equivalent method of expressing nonlinearity) at most $2^{-x_0}$ …

On the two-sided Guionnet-Jones-Shlyakhtenko construction at level three
R Jayakumar
https://arxiv.org/abs/2510.00747 https://arxiv.org/pdf/2510.00747

On the two-sided guionnet-jones-shlyakhtenko construction at level three
We study the two-sided Guionnet-Jones-Shlyakhtenko construction applied to the group planar algebra $P(\mathcal{G})$ of a finite non-trivial group $\mathcal{G}$. This produces a sequence of von Neumann algebras $M^k$ for $k \geq 0$ with no natural inclusions. Focusing on level $k=3$, we show that the resulting von Neumann algebra $M^3$ is isomorphic to the interpolated free group factor $\LF{1+\frac{2(n-1)}{n^2}}$, where $n=|\mathcal{G}|$. %The proof highlights the free Poisson nature…

On Hardy spaces associated with the twisted Laplacian and sharp estimates for the corresponding wave operator
Riju Basak, K. Jotsaroop
https://arxiv.org/abs/2509.00327 https://

On Hardy spaces associated with the twisted Laplacian and sharp estimates for the corresponding wave operator
We prove various equivalent characterisations of the Hardy space $H^p_{\mathcal{L}}(\mathbb{C}^n)$ for $00$ on $H^p_{\mathcal{L}}(\mathbb{C}^n)$. M…

Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m k} p \to \Box^m p$
S{\o}ren Brinck Knudstorp
https://arxiv.org/abs/2510.00864 https://arxiv.org…

Knocking Down Boxes: The FMP for $\mathbf{K} \oplus \Box^{m+k} p \to \Box^m p$
It is a long-standing open problem whether modal logics of the form $\mathbf{K} \oplus \Box^n p \to \Box^m p$ for $n>m>1$ have the finite model property (FMP). We solve this by showing that any modal logic axiomatized by formulas of the form $\Box^n p \to \Box^m p$ where $n>m>1$ has the FMP.

Integrable Spherical Brane Model at Large $N$
Mohsen Gheisarieha, Ramtin M. Yazdi, Arash Arabi Ardehali
https://arxiv.org/abs/2509.23869 https://arxiv.org/…

Integrable Spherical Brane Model at Large $N$
We study one of the simplest integrable two-dimensional quantum field theories with a boundary: $N$ free non-compact scalars in the bulk, constrained non-linearly on the boundary to lie on an $(N-1)$-sphere of radius $1/\sqrt{g}$. The $N=1$ case reduces to the single-channel Kondo problem, while larger $N$ is analogous to multi-channel or higher-spin impurity scenarios. Adding a boundary magnetic field -- a linear boundary coupling to the scalars -- enriches the model's structure while preservi…

On \'etale maps of sous-perfectoid adic spaces
Dmytro Rudenko
https://arxiv.org/abs/2509.25294 https://arxiv.org/pdf/2509.25294

On étale maps of sous-perfectoid adic spaces
We show that a map $\mathrm{Spa}\,B \to \mathrm{Spa}\,A$ of sous-perfectoid affinoid adic spaces is étale if and only if there exists a presentation $B \cong A\langle X_{1},\dots, X_{n} \rangle/(f_{1},\dots,f_{n})$ such that the determinant of the associated Jacobian matrix $\mathrm{det}( \frac{\partial f_{i}}{\partial X_{j}})_{1\leqslant i, j\leqslant n}$ is a unit in $B$. This allows us to provide some technical details to an important claim from the theory of étale maps of perfectoid space…

Three-fold Superstructured Superlattice HfN/HfAlN Thin Films for Enhanced Toughness
M. Lorentzon, R. Hahn, J. Palisaitis, H. Riedl, L. Hultman, J. Birch, N. Ghafoor
https://arxiv.org/abs/2510.00716

Three-fold Superstructured Superlattice HfN/HfAlN Thin Films for Enhanced Toughness
To simultaneously achieve high hardness and high toughness in protective coatings remains a fundamental challenge. Here, we harness the superlattice architecture to combine Koehler hardening while the coherent interfaces reduce the crack driving force and improve toughness, enabling coatings that are both hard and damage tolerant. We design and fabricate epitaxial HfN$_{1.33}$/Hf$_{0.76}$Al$_{0.24}$N$_{1.15}$ superlattices, deposited on MgO(001) substrates using low-energy, high-flux ion-assist…

Fixed, thanks to @…
With and without less(1):
pkg query --evaluate '%o ~ base/*' '%o\n\n%e\n\n----\n\n' | less
pkg query --evaluate '%o ~ base/*' '%o\n\n%e\n\n----\n\n'
#FreeBSD

Crosslisted article(s) found for cond-mat.soft. https://arxiv.org/list/cond-mat.soft/new
[1/1]:
- Coupling free-surface geometry and localized ion dose for continuum models of radiation-induced n...
Tyler P. Evans, Scott A. Norris

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- Nontrivial Solutions to a Cubic Identity and the Factorization of $n^2 n 1$
Hajrudin Fejzi\'c

Trump Advisers Have Discussed a Job for Adams to Quit Mayor's Race (New York Times)
https://www.nytimes.com/2025/09/03/nyregion/trump-adams-sliwa-quit-nyc-mayor.html?unlocked_article_code=1.jE8.1vby.99eyhvwznQvY&smid=url-share
http://www.memeorandum.com/250903/p88#a250903p88

On Kotzig's conjecture in random graphs
Stefan Glock, Amedeo Sgueglia
https://arxiv.org/abs/2510.01949 https://arxiv.org/pdf/2510.01949

On Kotzig's conjecture in random graphs
In 1963, Anton Kotzig famously conjectured that $K_{n}$, the complete graph of order $n$, where $n$ is even, can be decomposed into $n-1$ perfect matchings such that every pair of these matchings forms a Hamilton cycle. The problem is still wide open and here we consider a variant of it for the binomial random graph $G(n,p)$. We prove that, for every fixed $k$, there exists a constant $C=C(k)$ such that, when $p\ge \frac{C \log n}{n}$, with high probability, $G(n,p)$ contains $k$ edge-disjoint …

Terrorist (n): see Israeli settler. https://assortedflotsam.com/@NewsBot/115298233722842922

$p$-biharmonic Kirchhoff equations with critical Choquard nonlinearity
Divya Goel, Sarika Goyal, Diksha Saini
https://arxiv.org/abs/2509.00470 https://arxi…

$p$-biharmonic Kirchhoff equations with critical Choquard nonlinearity
In this article, we deal with the following involving $p$-biharmonic critical Choquard-Kirchhoff equation $$ \left(a+b\left(\int_{\mathbb R^N}|Δu|^p dx\right)^{θ-1}\right) Δ_{p}^{2}u = α\left(|x|^{-μ}*u^{p^*_μ}\right)|u|^{p^*_μ-2}u+ λf(x) |u|^{r-2} u \; \text{in}\; \mathbb R^N, $$ where $a\geq 0$, $b> 0$, $0<μ2p$, $p\geq 2$, $θ\geq1$, $α$ and $λ$ are positive real parameters, $p_μ^{*}= \frac{p(2N-μ)}{2(N-2p)}$ is the upper cr…

Classical BV cohomology of the $N=1$ spinning particle
Eugenia Boffo, Martin Cederwall
https://arxiv.org/abs/2510.00655 https://arxiv.org/pdf/2510.00655

Classical BV cohomology of the $N=1$ spinning particle
We show that the classical Batalin--Vilkovisky cohomology at negative ghost number of the spinning particle, observed in ref. arXiv:1511.02135, is removed by a Koszul--Tate resolution involving saturation of Grassmann odd variables. The model thus satisfies the axioms of Felder and Kazhdan. The AKSZ formulation of the resolved model is described. We reveal partial information on the resolution of the constrained phase space, which involves resolving the parity-shifted tangent sheaf of the light…

Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums
S. Sriram, A. David Christopher
https://arxiv.org/abs/2509.26559

Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums
Let $n$ and $t$ be positive integers with $t\geq 2$. Let $R_t(n)$ be the number of $t$-regular partitions of $n$. A class of functions, denoted $τ_k(n)$, is defined as follows: \[q\prod_{m=1}^{\infty}(1-q^m)^k=\sum_{n=1}^{\infty}τ_k(n)q^n, \] where $k$ is an integer. We express $τ_k(n)$ as a binomial coefficient weighted partition sum. Consequently, we obtain congruence identities that relate $τ_k(n)$, $R_t(n)$ and partition function weighted composition sums.

Generalized Parallel Scaling with Interdependent Generations
Harry Dong, David Brandfonbrener, Eryk Helenowski, Yun He, Mrinal Kumar, Han Fang, Yuejie Chi, Karthik Abinav Sankararaman
https://arxiv.org/abs/2510.01143

Generalized Parallel Scaling with Interdependent Generations
Parallel LLM inference scaling involves sampling a set of $N>1$ responses for a single input prompt. However, these $N$ parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent resp…

Explicit Constructions of Maximal 3-Zero-Sum-Free Subsets in $(\mathbb{Z}/4\mathbb{Z})^n$
Alfonso Davila Vera
https://arxiv.org/abs/2509.01735 https://arxi…

Explicit Constructions of Maximal 3-Zero-Sum-Free Subsets in $(\mathbb{Z}/4\mathbb{Z})^n$
We address Nathan Kaplan's 2014 CANT problem: the largest $H \subseteq (\mathbb{Z}/4\mathbb{Z})^n$ with no distinct $x, y, z \in H$ such that $x + y + z \equiv 0 \pmod{4}$. A universal optimal construction, $H = \{ v \mid v_1 \equiv 1 \text{ or } 3 \pmod{4} \}$, achieves size $4^n/2$ and density 0.5 for all $n$, proven maximal via $|H|^2 \leq (4^n - |H|) \cdot |H|$. Verified computationally to $n=10$; code at https://github.com/DynMEP/ZeroSumFreeSets-Z4/releases/ta…

The Kernel and Image of Orbit Homomorphisms for the Witt Algebra
Tuan Anh Pham, James Timmins
https://arxiv.org/abs/2510.00756 https://arxiv.org/pdf/2510.0…

The Kernel and Image of Orbit Homomorphisms for the Witt Algebra
The Witt algebra $W_{\geq -1}$ is the Lie algebra of algebraic vector fields on a line. We investigate the two-sided ideal structure of its universal enveloping algebra, by studying the orbit homomorphisms $Ψ_n: U(W_{\geq -1}) \rightarrow T_n$, an infinite family of homomorphisms to noncommutative Noetherian algebras. The orbit homomorphisms lift primitive ideals from solvable Lie algebras to $U(W_{\geq -1})$, thereby playing a central role in the orbit method for the Witt algebra. We prove th…

An alternative bootstrap procedure for factor-augmented regression models
Peiyun Jiang, Takashi Yamagata
https://arxiv.org/abs/2510.00947 https://arxiv.org…

An alternative bootstrap procedure for factor-augmented regression models
In this paper, we propose a novel bootstrap algorithm that is more efficient than existing methods for approximating the distribution of the factor-augmented regression estimator for a rotated parameter vector. The regression is augmented by $r$ factors extracted from a large panel of $N$ variables observed over $T$ time periods. We consider general weak factor (WF) models with $r$ signal eigenvalues that may diverge at different rates, $N^{α_{k}}$, where $0<α_{k}\leq 1$ for $k=1,2,...,r$. We…

Theory for the spectral splitting exponent of exceptional points
Shu-Xuan Wang, Zhongbo Yan
https://arxiv.org/abs/2509.02174 https://arxiv.org/pdf/2509.021…

Theory for the spectral splitting exponent of exceptional points
Exceptional points (EPs), singularities in non-Hermitian systems where eigenvalues and eigenstates coalesce, exhibit a dramatically enhanced response to perturbations compared to Hermitian degeneracies. This makes them exceptional candidates for sensing applications. The spectral splitting of an $N$th-order EP scales with perturbation strength $ε$ over a wide range, from $ε$ to $ε^{1/N}$. Although the exact scaling exponent can be determined in principle by solving the characteristic equatio…

Differentially Private Learning of Exponential Distributions: Adaptive Algorithms and Tight Bounds
Bar Mahpud, Or Sheffet
https://arxiv.org/abs/2510.00790 https://

Differentially Private Learning of Exponential Distributions: Adaptive Algorithms and Tight Bounds
We study the problem of learning exponential distributions under differential privacy. Given $n$ i.i.d.\ samples from $\mathrm{Exp}(λ)$, the goal is to privately estimate $λ$ so that the learned distribution is close in total variation distance to the truth. We present two complementary pure DP algorithms: one adapts the classical maximum likelihood estimator via clipping and Laplace noise, while the other leverages the fact that the $(1-1/e)$-quantile equals $1/λ$. Each method excels in a d…

On the connectedness of the boundary of hierarchically hyperbolic spaces
Ravi Tomar
https://arxiv.org/abs/2509.00321 https://arxiv.org/pdf/2509.00321

On the connectedness of the boundary of hierarchically hyperbolic spaces
We prove that, under a mild assumption, any metrizable compactification of a one-ended proper geodesic metric space is connected. As a consequence, we deduce that the boundary, introduced by Durham--Hagen--Sisto, of a one-ended hierarchically hyperbolic space is connected. Moreover, we prove that the connectedness of the boundary of a hierarchically hyperbolic group is equivalent to the one-endedness of the group. As an application, we show that if, for $n\geq 2$, $G_1=A_1\ast\dots\ast A_n$ and…

Partially hyperbolic flows on flat vector bundles with an application to complete affine manifolds
Suhyoung Choi
https://arxiv.org/abs/2509.26117 https://a…

Partially hyperbolic flows on flat vector bundles with an application to complete affine manifolds
Let $N$ be a manifold of dimension $m$ with a flat vector bundle given by a representation $ρ:π_1(N) \rightarrow \mathrm{GL}(n, \mathbf{R})$ where $π_1(N)$ is finitely generated. The holonomy group $ρ$ is a $k$-partially hyperbolic holonomy representation if the flat bundle pulled back over the unit tangent bundle of a sufficiently large compact submanifold of $N$ splits into expanding, neutral, and contracting subbundles along the geodesic flow, where the expanding and contracting subbundl…

Primes of the form $ax by$ in certain intervals with small solutions
Yuchen Ding, Takao Komatsu, Honghu Liu
https://arxiv.org/abs/2510.01781 https://arxiv.…

Primes of the form $ax+by$ in certain intervals with small solutions
Let $1

Regularity of cylindrical singular sets of mean curvature flow
Ao Sun, Zhihan Wang, Jinxin Xue
https://arxiv.org/abs/2509.01707 https://arxiv.org/pdf/2509.…

Regularity of cylindrical singular sets of mean curvature flow
In this paper, we study the $k$-cylindrical singular set of mean curvature flow in $\mathbb R^{n+1}$ for each $1\leq k\leq n-1$. We prove that they are locally contained in a $k$-dimensional $C^{2,α}$-submanifold after removing some lower-dimensional parts. Moreover, if the $k$-cylindrical singular set is a $k$-submanifold, then its curvature is determined by the asymptotic profile of the flow at these singularities. As a byproduct, we provide a detailed asymptotic profile and graphical radius…

Replaced article(s) found for cond-mat.soft. https://arxiv.org/list/cond-mat.soft/new
[1/1]:
- Combinatorial Design of Floppy Modes and Frustrated Loops in Metamaterials
Wenfeng Liu, Tomer A. Sigalov, Corentin Coulais, Yair Shokef

Explicit construction of infinite families of strongly regular digraphs with parameters $((v (2^{n 1}-4)t)2^{n-1}, k (2^n-2)t, t, \lambda, t)$
Viktor A. Byzov, Igor A. Pushkarev
https://arxiv.org/abs/2509.25425

Explicit construction of infinite families of strongly regular digraphs with parameters $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$
An explicit construction of infinite sequences of strongly regular digraphs with parameter sets $((v+(2^{n+1}-4)t)2^{n-1}, k+(2^n-2)t, t, λ, t)$ is described. A computer program was used to find the initial digraphs. The remaining terms of the sequence are obtained by the constructed recurrence. Using the described approach, 11 families of strongly regular digraphs were found. In particular, these families contain digraphs $\text{dsrg}(72, 18, 5, 3, 5)$, $\text{dsrg}(76, 19, 5, 4, 5)$, $\text{…

Borel Kernels in Borel Directed Graphs
Ruijun Wang
https://arxiv.org/abs/2509.01948 https://arxiv.org/pdf/2509.01948

Borel Kernels in Borel Directed Graphs
We prove that there is a Borel quasi-kernel in any locally countable Borel directed graph with finite Borel chromatic number. We prove that the Borel chromatic number of a Borel directed graph with bounded out-degree $n$ is either infinite or less than or equal to $\frac{(n+1)(n+2)}{2}$. This is an alternative proof of Palamourdas' theorem.

Finite $N$ precursors of the free cumulants
Sylvain Lacroix, Jean-Bernard Zuber
https://arxiv.org/abs/2508.21483 https://arxiv.org/pdf/2508.21483

Finite $N$ precursors of the free cumulants
We introduce $\mathrm{U}(N)$ invariant polynomials on the space of $N\times N$ matrices that are precursors of free cumulants in various respects. First, they are polynomials of deterministic matrices, that are not yet evaluated over some probability law, contrary to what is usually meant by cumulants. Secondly, they converge towards the algebraic expression of free cumulants in terms of moments as $N\to \infty$, with $1/N^2$ corrections expressed in terms of monotone Hurwitz numbers. Their mos…

Well-posedness and scattering of odd solutions for the defocusing INLS in one dimension
Zhi-Yuan Cui, Yuan Li, Dun Zhao
https://arxiv.org/abs/2509.02158 https://

Well-posedness and scattering of odd solutions for the defocusing INLS in one dimension
We consider the defocusing inhomogeneous nonlinear Schrödinger equation $i\partial_tu+Δu= |x|^{-b}|u|^αu,$ where $0

Bounds on two-distance sets in Euclidean space and Unit Sphere
Wei-Chun Chen, Wei-Hsuan Yu
https://arxiv.org/abs/2509.00858 https://arxiv.org/pdf/2509.0085…

Bounds on two-distance sets in Euclidean space and Unit Sphere
We establish upper bounds for the size of two-distance sets in Euclidean space and spherical two-distance sets. The main recipe for obtaining upper bounds is the spectral method. We construct Seidel matrices to encode the distance relations and apply eigenvalue analysis to obtain explicit bounds. For Euclidean space, we have the upper bounds for the cardinality $n$ of a two-distance set. \[ n \le \dfrac{(d+1)\left(\left(\frac{1+δ^2}{1-δ^2}\right)^2 - 1\right)}{\left(\frac{1+δ^2}{1-δ^2}\…

Elliptic surfaces to class groups and Selmer groups
Kalyan Banerjee, Kalyan Chakraborty, Azizul Hoque
https://arxiv.org/abs/2509.00551 https://arxiv.org/pd…

Elliptic surfaces to class groups and Selmer groups
In this note, we connect the $n$-torsions of the Picard group of an elliptic surface to the $n$-divisibility of the class group of torsion fields for a given integer $n>1$. We also connect the $n$-divisibility of the Selmer group to that of the class group of torsion fields.

Equal knapsack identities between symmetric group character degrees
David J. Hemmer, Armin Straub, Karlee J. Westrem
https://arxiv.org/abs/2510.00301 https://

Equal knapsack identities between symmetric group character degrees
We prove a series of ``knapsack'' type equalities for irreducible character degrees of symmetric groups. That is, we find disjoint subsets of the partitions of $n$ so that the two corresponding character-degree sums are equal. Our main result refines our recent description of the Riordan numbers as the sum of all character degrees $f^λ$ where $λ$ is a partition of $n$ into three parts of the same parity. In particular, the sum of the ``fat-hook'' degrees $f^{(k,k,1^{n-2k})}+f^{(k+1,k+1,1^{n-2…

The exterior derivative and the mean value equality in $\mathbb{R}^n$
Daniel Fadel, Henrique N. S\'a Earp, Tom\'as S. R. Silva
https://arxiv.org/abs/2510.00999 https://

The exterior derivative and the mean value equality in $\mathbb{R}^n$
This survey revisits classical results in vector calculus and analysis by exploring a generalised perspective on the exterior derivative, interpreting it as a measure of "infinitesimal flux". This viewpoint leads to a higher-dimensional analogue of the Mean Value Theorem, valid for differential $k$-forms, and provides a natural formulation of Stokes' theorem that mirrors the exact hypotheses of the Fundamental Theorem of Calculus - without requiring full $C^1$ smoothness of the differential for…

A note on the distribution of the sum of lengths of the initial longest increasing sequences in cycles of random permutations
Ljuben Mutafchiev
https://arxiv.org/abs/2509.26129 …

A note on the distribution of the sum of lengths of the initial longest increasing sequences in cycles of random permutations
Let $S_n$ be the set of all permutations of $\{1,2,\ldots,n\}$ and let $σ=(σ_1,σ_2,\ldots,σ_n)\in S_n$. The {\it initial longest increasing sequence} (ILIS) in $σ$ has length $m$ if, for $1\le m\le n-1$, $σ_1<σ_2<\ldots<σ_m, σ_m>σ_{m+1}$, and has length $n$ if $σ=(1,2,\ldots,n)$. Let $l(σ)$ be the length of the ILIS in $σ$. We assume that $σ$ is represented in cycle notation, so that the first number in each cycle is the minimum number of this cycle. We also assume that $σ$ is ch…

Forcing Axioms and construction schemes
Jorge Antonio Cruz Chapital, Osvaldo Guzman, Stevo Todorcevic
https://arxiv.org/abs/2509.01712 https://arxiv.org/pd…

Forcing Axioms and construction schemes
We continue the development of the theory of construction schemes over $ω_1$ as introduced by the third author by studying their relation with forcing axioms. Formally, we introduce the cardinals $\mathfrak{m}^n_{\mathcal{F}}$ and use the consistency of $\mathfrak{m}^2_\mathcal{F}>ω_1$ to prove a fundamental result relating gaps and almost disjoint families over $ω$. The cardinals $\mathfrak{m}_\mathcal{F}$ are also used to prove some limiting results for contstruction schemes, some of which…

Tight Bounds for Cycle-Edge Decompositions and Covers
Saieed Akbari, Jonny Aloni, Arash Beikmohammadi, Alexander Clow
https://arxiv.org/abs/2509.01901 https://

Tight Bounds for Cycle-Edge Decompositions and Covers
An old conjecture of Gallai states that every $n$ vertex graph can be decomposed, that is $E(G)$ can be partitioned, into $\lceil \frac{n}{2}\rceil$ or fewer paths. In response to this conjecture, Lovász proved in 1968 that every $n$ vertex graph can be decomposed into $\lfloor \frac{n}{2}\rfloor$ or fewer cycles and paths. We study a related conjecture which states that every $n$ vertex graph can be decomposed into $n-1$ or fewer cycles and edges. We prove this conjecture for all graphs with …

The trigonometric polynomial on sums of two squares, an additive problem and generalisation
Olivier Ramare, GK Viswanadham
https://arxiv.org/abs/2509.23260 https://

The trigonometric polynomial on sums of two squares, an additive problem and generalisation
Let $B$ be the set of odd integers that are sums of two coprime squares. We prove that the trigonometric polynomial $S(α;N)=\sum_{b\in B,b\leq N} e(bα)$ satisfies \[ \frac{S(α; N)}{N/\sqrt{\log N}}<<_{A,A'} \frac{1}{ϕ(q)} + \sqrt{\frac{q}{N}}(\log N)^{7} +\frac{1}{(\log N)^A} \] for any $A,A'\geq 0$ and when $(a,q)=1$ and $|qα-a|\leq (\log N)^{A'}/N$. We use this estimate together with a variant of the circle method influenced by Green and Tao's Transference Principle to obtain t…

Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
Junming Xie
https://arxiv.org/abs/2509.01023 https://arxiv.org/pd…

Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
In this paper, we investigate the convexity of mean convex asymptotically conical self-expanders to the mean curvature flow in $\mathbb{R}^{n+1}$. Specifically, for $n\geq 3$, we show that any $n$-dimensional complete mean convex self-expander asymptotic to mean convex and weakly convex cones must be strictly convex.

A Study of Fibonacci Cordial Labeling in Structured Graph Families
Sarbari Mitra, Soumya Bhoumik
https://arxiv.org/abs/2509.01823 https://arxiv.org/pdf/250…

A Study of Fibonacci Cordial Labeling in Structured Graph Families
A \emph{Fibonacci cordial labeling} of a graph \( G \) is an injective function \( f: V(G) \rightarrow \{F_0, F_1, \dots, F_n\} \), where \( F_i \) denotes the \( i^{\text{th}} \) Fibonacci number, such that the induced edge labeling \( f^*: E(G) \rightarrow \{0,1\} \), given by \( f^*(uv) = (f(u) + f(v)) \) $(\bmod\ 2)$, satisfies the balance condition \( |e_f(0) - e_f(1)| \le 1 \). Here, \( e_f(0) \) and \( e_f(1) \) represent the number of edges labeled 0 and 1, respectively. A gra…

Irreducibility and locus of complex roots of polynomials related to Fermat's Last Theorem
Hayk Karapetyan, Ruben Hambardzumyan
https://arxiv.org/abs/2510.00020 https://

Irreducibility and locus of complex roots of polynomials related to Fermat's Last Theorem
We investigate the polynomials $x^n + (1-x)^n + a^n$, a rational root of which would provide a counterexample to Fermat's Last Theorem. We consider the more general question of their irreducibility and prove that in some cases. We investigate the location of complex roots of these polynomials, and prove that for some $a \in \mathbb{Q}$, the roots lie on explicitly given curves while being dense in those curves.

On the chromatic number of random triangle-free graphs
Clayton Mizgerd, Will Perkins, Yuzhou Wang
https://arxiv.org/abs/2509.01376 https://arxiv.org/pdf/25…

On the chromatic number of random triangle-free graphs
We study the chromatic number of typical triangle-free graphs with $Θ\left( n^{3/2} (\log n)^{1/2} \right)$ edges and establish the width of the scaling window for the transitions from $χ= 3$ to $χ= 4$ and from $χ= 4$ to $χ= 5$. The transition from $3$- to $4$-colorability has scaling window of width $Θ(n^{4/3} (\log n)^{-1/3})$. To prove this, we show a high probability equivalence of the $3$-colorability of a random triangle-free graph at this density and the satisfiability of an inst…

Perfect $F$-gauges and finite flat group schemes
Keerthi Madapusi, Shubhodip Mondal
https://arxiv.org/abs/2509.01573 https://arxiv.org/pdf/2509.01573

Perfect $F$-gauges and finite flat group schemes
We show an equivalence of categories, over general $p$-adic bases, between finite locally $p^n$-torsion commutative group schemes and $\Int/p^n\Int$-modules in perfect $F$-gauges of Tor amplitude $[-1,0]$ with Hodge-Tate weights $0,1$. By relating fppf cohomology of group schemes and syntomic cohomology of $F$-gauges, we deduce some consequences: These include the representability of relative fppf cohomology of finite flat group schemes under proper smooth maps of $p$-adic formal schemes, as we…

On the Precise Asymptotics of $ex(n,n,n,K_{2,t})$ for even $t$
Zilin Luo
https://arxiv.org/abs/2509.21756 https://arxiv.org/pdf/2509.21756

On the Precise Asymptotics of $ex(n,n,n,K_{2,t})$ for even $t$
Let $K_{2,t}$ denote the complete bipartite graph. For an integer $n\ge 1$, let $ex(n,n,n,K_{2,t})$ be the maximum number of edges in an $n\times n\times n$ tripartite graph (that is, a 3-partite graph with three parts each of size $n$) containing no copy of $K_{2,t}$. In this paper we prove that, for even $t\ge 2$, $$ ex(n,n,n,K_{2,t}) \ge \frac{3\sqrt{t-1}}{\sqrt{2}}\, n^{3/2} + o(n^{3/2}). $$ Combining our construction with earlier work of Tait and Timmons, we obtain $$ \lim\limits_{n\to\inf…

Convergence exponent of Dirichlet non-improvable numbers in the theory of continued fractions
Xiaoyan Tan, Zhenliang Zhang
https://arxiv.org/abs/2509.23059 https://

Convergence exponent of Dirichlet non-improvable numbers in the theory of continued fractions
Let $x \in [0,1)$ be an irrational number with continued fraction expansion $[a_1(x),a_2(x), \cdots,a_n(x),\cdots]$ and $q_n(x)$ be the denominator of its $n$-th convergent. We establish, for any $α,β$ in $[0,+\infty]$, the Hausdorff dimension formula of the intersections of the sets of Dirichlet non-improvable numbers and the level set of convergent exponent, i.e. $$ G(α,β): =\left\{x\in[0,1)\colon τ(x)=α,\,\,\text{and} \,\, \limsup_{n\to\infty}\frac{\log (a_n(x)a_{n+1}(x))}{\log q_n(x…

On lower bounds for the distances between APN functions
Maria Mihaila, Darrion Thornburgh
https://arxiv.org/abs/2509.02280 https://arxiv.org/pdf/2509.02280…

On lower bounds for the distances between APN functions
Whether two distinct APN functions can have a Hamming distance of $1$ remains an open problem. In 2020, L. Budaghyan et al. introduced a new CCZ-invariant $Π_F$ which can be used to provide lower bounds on the Hamming distance between a given APN function $F \colon \mathbb{F}_2^n \to \mathbb{F}_2^n$ and other APN functions. Lower bounds on the distance from an APN function $F$ to any other are known for almost bent (AB) functions and when $F$ is a 3-to-1 quadratic function with $n$ even. In th…

Polynomials and asymptotic constants in a resurgent problem from 't Hooft
David Broadhurst
https://arxiv.org/abs/2509.26297 https://arxiv.org/pdf/2509.…

Polynomials and asymptotic constants in a resurgent problem from 't Hooft
In a recent study of the quantum theory of harmonic oscillators, Gerard 't Hooft proposed the following problem: given $G(z)=\sum_{n>0}\sqrt{n}z^n$ for $|z|<1$, find its analytic continuation for $|z|\ge1$, excluding a branch-cut $z\in[1,\,\infty)$. A solution is provided by the bilateral convergent sum $G(z)=\frac12\sqrtπ\sum_{n\in{\mathbb Z}}(2nπ{\rm i}-\log(z))^{-3/2}$. On the negative real axis, $G(-e^u)$ has a sign-constant asymptotic expansion in $1/u^2$, for large p…

There are siblings of $\chi$ which are permutations for $n$ even
Bj\"orn Kriepke (University of Rostock), Gohar Kyureghyan (University of Rostock)
https://arxiv.org/abs/2509.24839

There are siblings of $χ$ which are permutations for $n$ even
Let $1$ be the all-one vector and $\odot$ denote the component-wise multiplication of two vectors in $\mathbb F_2^n$. We study the vector space $Γ_n$ over $\mathbb F_2$ generated by the functions $γ_{2k}:\mathbb F_2^n \to \mathbb F_2^n, k\geq 0$, where $$ γ_{2k} = S^{2k}\odot(1+S^{2k-1})\odot(1+S^{2k-3})\odot\ldots\odot(1+S) $$ and $S:\mathbb F_2^n\to\mathbb F_2^n$ is the cyclic left shift function. The functions in $Γ_n$ are shift-invariant and the well known $χ$ function used in several …

On new proper Jordan schemes related to quaternion and octonion algebras
Akihide Hanaki, Masayoshi Yoshikawa
https://arxiv.org/abs/2509.01865 https://arxiv…

On new proper Jordan schemes related to quaternion and octonion algebras
We present a construction of a Jordan scheme from an elementary abelian $2$-group of rank $n$ and a $\{1,-1\}$-matrix of order $2^n$ that satisfies a specified condition. We then prove that the orders of matrices with the specified condition are limited to $2, 4$ or $8$. Using these matrices, we construct essentially two new proper Jordan schemes of orders $16$ and $32$. Finally, we analyze the structures of the real adjacency Jordan algebras of these Jordan schemes and prove that they are the …

On Graphical Partitions with Restricted Parts
Gilead Levy
https://arxiv.org/abs/2510.00007 https://arxiv.org/pdf/2510.00007

On Graphical Partitions with Restricted Parts
We study the distributions of parts in random integer partitions subject to general arithmetic restrictions. In particular, we enumerate restricted graphical partitions of an even integer $n$ and identify the conditions under which the fraction of graphical partitions, relative to all restricted partitions, is maximal. We prove that this maximal fraction is asymptotically $O(n^{-1/2})$. Furthermore, for any set of arithmetic restrictions, we establish the existence of a minimal lower bound on t…

Ramsey numbers of long even cycles versus books
Qizhong Lin, Shixi Song
https://arxiv.org/abs/2509.26323 https://arxiv.org/pdf/2509.26323

Ramsey numbers of long even cycles versus books
For any positive integers $k$ and $n$, let $B_n^{(k)}$ be the book graph consisting of $n$ copies of the complete graph $K_{k+1}$ sharing a common $K_k$. Let $C_m$ be a cycle of length $m$. Prior work by Allen, Łuczak, Polcyn, and Zhang (2023) established the Ramsey number $R(C_{m},B_n^{(1)})$ for all sufficiently large even integer $m = Ω(n^{9/10})$. Recently, Hu, Lin, Łuczak, Ning, and Peng (2025) obtained the exact value of $R(C_{m},B_n^{(2)})$ under the same asymptotic conditions. A natu…

On irrationals with Lagrange value exactly 3
Zhe Cao, Harold Erazo, Carlos Gustavo Moreira
https://arxiv.org/abs/2509.01867 https://arxiv.org/pdf/2509.0186…

On irrationals with Lagrange value exactly 3
For $c>0$, let $X_c$ denote the set of $x\in\mathbb{R}\backslash\mathbb{Q}$ such that $\left| x-\frac{p}{q} \right|<\frac{1}{cq^2}$ has only finitely many rational solutions $\frac{p}{q}$. It is a classical fact, known since the 1950s, that $X_c$ is uncountable for $c>3$ and countable for $c<3$. However, the cardinality of $X_3$ does not appear to be present in the literature. We prove that $X_3$ is uncountable. More generally, we show that for any $n\in\mathbb{N}\cup\{\infty\}$, th…

Monochromatic components with many edges in random graphs
Hannah Fox, Sammy Luo
https://arxiv.org/abs/2509.01766 https://arxiv.org/pdf/2509.01766

Monochromatic components with many edges in random graphs
In an $r$-coloring of edges of the complete graph on $n$ vertices, how many edges are there in the largest monochromatic connected component? A construction of Gyárfás shows that for infinitely many values of $r$, there exist colorings where all monochromatic components have at most $\left(\frac{1}{r^2-r}+o(1)\right)\binom{n}{2}$ edges. Conlon, Luo, and Tyomkyn conjectured that components with at least this many edges are attainable for all $r \ge 3$. Conlon, Luo, and Tyomkyn proved this conj…

Decidability of polynomial equations over function fields in positive characteristic
Nicolas Daans
https://arxiv.org/abs/2509.02290 https://arxiv.org/pdf/2…

Decidability of polynomial equations over function fields in positive characteristic
Let $K$ be a field of positive characteristic with no algebraically closed subfield. Let $F$ be a function field over $K$ and $t \in F$ transcendental over $K$. Refining a result of Eisentr{ä}ger and Shlapentokh, we show that there is no algorithm which, on input a polynomial $f \in \mathbb{Z}[t][X_1, \ldots, X_n]$, determines whether $f$ has a zero in $F^n$. To this end, we revisit and partially extend several recent results from the literature on existential definability in function fields.

The odd independence number of graphs, II: Finite and infinite grids and chessboard graphs
Yair Caro, Mirko Petru\v{s}evski, Riste \v{S}krekovski, Zsolt Tuza
https://arxiv.org/abs/2510.01897

The odd independence number of graphs, II: Finite and infinite grids and chessboard graphs
An odd independent set $S$ in a graph $G=(V,E)$ is an independent set of vertices such that, for every vertex $v \in V \setminus S$, either $N(v) \cap S = \emptyset$ or $|N(v) \cap S| \equiv 1$ (mod 2), where $N(v)$ stands for the open neighborhood of $v$. The largest cardinality of odd independent sets of a graph $G$, denoted $α_{od}(G)$, is called the odd independence number of $G$. This new parameter is a natural companion to the recently introduced strong odd chromatic number. …

On the maximal size of $(a,b)$-town$\pmod k$ families
Nikola Veselinov, Miroslav Marinov
https://arxiv.org/abs/2510.00251 https://arxiv.org/pdf/2510.00251

On the maximal size of $(a,b)$-town$\pmod k$ families
A family $\mathcal{F}\subseteq\mathcal{P}(n)$ is an $(a,b)$-town$\pmod k$ if all sets in it have cardinality $a\pmod k$ and all pairwise intersections in it have cardinality $b\pmod k$. For $k=2$ the maximal size of such a family is known for each $a,b$, while for $k=3$ only $b-a\equiv 2 \pmod 3$ is fully understood. We provide a bound for $k=3$ when $b-a\equiv 1 \pmod 3$ and $n\equiv 2 \pmod 3$, which turns out to be tight for infinitely many such $n$. We also give sufficient conditions on the…

Tensor rank of the determinant and periodic triangulations of $\mathbb{R}^n$
Sergey Avvakumov, Roman Karasev
https://arxiv.org/abs/2509.22333 https://arxiv…

Tensor rank of the determinant and periodic triangulations of $\mathbb{R}^n$
We prove that in any $\mathbb{Z}^n$-periodic triangulation of $\mathbb{R}^n$ the number of $\mathbb{Z}^n$-orbits of $n$-dimensional simplices is at least the tensor rank of the $n$th determinant tensor. The latter is known to be at least $\frac{n^{n-1}}{(n-1)!}$, which is approximately $\frac{e^n}{\sqrt{2πn}}$ for large $n$. The triangulation is not assumed to be geometric, meaning that its simplices can be ``curved''. We also provide lower bounds for general spaces. A simplicial cell comple…

Improved Bounds on Diffsequences with Gaps in Powers of 2
Kanav Talwar, Utkarsh Gupta
https://arxiv.org/abs/2508.21280 https://arxiv.org/pdf/2508.21280

Improved Bounds on Diffsequences with Gaps in Powers of 2
Let $D$ be a set of positive integers. A $D$-diffsequence of length $k$ is a sequence of positive integers $a_1 < \cdots < a_k$ such that $a_{i+1}-a_i\in D$ for $i=1,\ldots,k-1$. For $D=\{2^i\mid i\in \mathbb{Z}_{\ge 0}\}$, it is known that there exists a minimum integer $n$, denoted by $Δ(D,k)$, such that every $2$-coloring of $\{1,\ldots n \}$ admits a monochromatic $D$-diffsequence of length $k$. In this work, we prove a new lower bound for $Δ(D,k)$ to $Δ(D,k)\ge \left(\sqrt{\frac{8k-5}{1…

On the Characteristic polynomial of ABS Matrix and ABS-Energy of Some Graphs
Sharad Barde, Ganesh Mundhe, Mayur Kshirsagar, A. N. Bhavale
https://arxiv.org/abs/2509.02155 https:…

On the Characteristic polynomial of ABS Matrix and ABS-Energy of Some Graphs
For a graph $G$ with $n$ vertices and $m$ edges, Lin \textit{et al.} \cite{Lin} define the \textit{atom--bond sum-connectivity} ($ABS$) matrix of $G$ such that the $(i,j)^{\text{th}}$ entry is \[ \sqrt{1 - \frac{2}{d_i + d_j}} \] if vertex $v_i$ is adjacent to the vertex $v_j$, and $0$ otherwise. In this article, we determine the characteristic polynomial of the $ABS$ matrix for certain specific classes of graphs. Furthermore, we compute the $ABS$ eigenvalues and the $ABS$ energy for these clas…

Latin squares with three disjoint subsquares of the same order
Tara Kemp, James G. Lefevre
https://arxiv.org/abs/2510.00364 https://arxiv.org/pdf/2510.0036…

Latin squares with three disjoint subsquares of the same order
Given an integer partition $P = (h_1h_2\dots h_k)$ of $n$, a realization of $P$ is a latin square with disjoint subsquares of orders $h_1,h_2,\dots,h_k$. Most known results restrict either $k$ or the number of different integers in $P$. There is little known for partitions with arbitrary $k$ and subsquares of at least three orders. It has been conjectured that if $h_1=h_2=h_3\geq h_4\geq\dots\geq h_k$ then a realization of $P$ always exists. We prove this conjecture, and thus show the existence…

Improved upper bounds on color reversal by local inversions
Kumud Singh Porte, RB Sandeep, Kamal Santra
https://arxiv.org/abs/2510.00149 https://arxiv.org/…

Improved upper bounds on color reversal by local inversions
We study the problem of color reversal in bicolored graphs under local inversions. A \emph{bicoloration} of a graph $G=(V,E)$ is a mapping $β: V \to \{-1,1\}$. A \emph{local inversion} at a vertex $v \in V$ consists of reversing the colors of all neighbors of $v$ and replacing the subgraph induced by these neighbors with its complement, while leaving $v$ and the rest of $G$ unchanged. Sabidussi (Discrete Mathematics, 1987) showed that any bicolored graph on $n$ vertices without isolated vertic…

On the Number of Path Systems
Daniel Cizma, Nati Linial
https://arxiv.org/abs/2508.21379 https://arxiv.org/pdf/2508.21379

On the Number of Path Systems
A path system in a graph $G$ is a collection of paths, with exactly one path between any two vertices in $G$. A path system is said to be consistent if it is intersection-closed. We show that the number of consistent path systems on $n$ vertices is $n^{\frac{n^2}{2}(1-o(1))}$, whereas the number of consistent path systems which are realizable as the unique geodesics w.r.t. some metric is only $2^{Θ(n^2)}$. In addition, these insights allow us to improve known bounds on the face-count of the …

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Characterisation of the big Ramsey degrees of the generic partial order
Balko, Chodounsk\'y, Dobrinen, Hubi\v{c}ka, Kone\v{c}n\'y, Vena, Zucker

Generalizations of Ferber-Krivelevich and Gallai Theorems on parity of degrees in induced subgraphs
Jiangdong Ai, Qiwen Guo, Gregory Gutin, Yimin Hao, Anders Yeo
https://arxiv.org/abs/2509.01428

Generalizations of Ferber-Krivelevich and Gallai Theorems on parity of degrees in induced subgraphs
A long-standing and well-known conjecture (see e.g. Caro, Discrete Math, 1994) states that every $n$-vertex graph $G$ without isolated vertices contains an induced subgraph where all vertices have an odd degree and whose order is linear in $n$. Ferber and Krivelevich (Adv. Math., 2022) confirmed the conjecture. In this short paper, we generalize this result by considering $G$ with vertices labeled 0 or 1 and requiring that in an induced subgraph of $G$, the 0-labeled vertices are of even degree…

Size of bipartite graphs with given diameter and connectivity constraints
Sonwabile Mafunda
https://arxiv.org/abs/2509.01825 https://arxiv.org/pdf/2509.018…

Size of bipartite graphs with given diameter and connectivity constraints
In the first part of this paper we determine the maximum size of a (finite, simple, connected) bipartite graph of given order, diameter $d$, and connectivity $κ$. It was shown by Ali, Mazorodze, Mukwembi and Vetrík [On size, order, diameter and edge-connectivity of graphs. Acta Math. Hungar. {\bf 152}, (2017)] that for a connected triangle-free graph of order $n$, diameter $d$ and edge-connectivity $λ$, the size is bounded from above by about $\frac{1}{4}\left(n-\frac{(λ+c) d}{2}\right)^2…