Tootfinder

This https://arxiv.org/abs/2501.12729 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the algebraic transfers of ranks 4 and 6 at generic degrees
Let $\mathscr A$ denote the classical singly-graded Steenrod algebra over the binary field $\mathbb Z/2.$ We write $P_k:=\mathbb Z/2[t_1, t_2, \ldots, t_k]$ as the polynomial algebra on $k$ generators, each having a degree of one. Let $GL_k$ be the general linear group of rank $k$ over $\mathbb Z/2.$ Then, $P_k$ is an $ \mathscr A[GL_k]$-module. The structure of the cohomology groups, ${\rm Ext}_{ \mathscr A}^{k, k+\bullet}(\mathbb Z/2, \mathbb Z/2)$, of the Steenrod algebra has, thus far, resi…

Star decompositions via orientations
Viktor Harangi
https://arxiv.org/abs/2506.05194 https://arxiv.org/pdf/2506.05194

Star decompositions via orientations
A $k$-star decomposition of a graph is a partition of its edges into $k$-stars (i.e., $k$ edges with a common vertex). The paper studies the following problem: given $k \leq d/2$, does the random $d$-regular graph have a $k$-star decomposition (asymptotically almost surely, provided that the number of edges is divisible by $k$)? Delcourt, Greenhill, Isaev, Lidický, and Postle proved the a.a.s. existence for every odd $k$ using earlier results regarding orientations satisfying certain degree co…

Three Hot Jupiters transiting K-dwarfs with a significant heavy element mass
Y. G. C. Frensch, F. Bouchy, G. Lo Curto, S. Ulmer-Moll, S. G. Sousa, N. C. Santos, K. G. Stassun, C. N. Watkins, H. Chakraborty, K. Barkaoui, M. Battley, W. Ceva, K. A. Collins, T. Daylan, P. Evans, J. P. Faria, C. Farret Jentink, E. Fontanet, E. Frid\'en, G. Furesz, M. Gillon, N. Grieves, C. Hellier, E. Jehin, J. M. Jenkins, L. K. W. Kwok, D. W. Latham, B. Lavie, N. Law, A. W. Mann, F. Murgas, E. Palle, …

Three Hot Jupiters transiting K-dwarfs with a significant heavy element mass
Albeit at a lower frequency than around hotter stars, short-period gas giants around low-mass stars ($T_\mathrm{eff} < 4965$ K) do exist, despite predictions from planetary population synthesis models that such systems should be exceedingly rare. By combining data from TESS and ground-based follow-up observations, we seek to confirm and characterize giant planets transiting K dwarfs, particularly mid/late K dwarfs. Photometric data were obtained from the TESS mission, supplemented by ground-bas…

This https://arxiv.org/abs/2506.01870 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Various irrational series involving binomial coefficients
Motivated by Galois theory, we propose some new irrational series of Ramanujan's type or Zeilberger's type. For example, we conjecture that \begin{equation*}\sum_{k=1}^\infty\frac{\binom{2k}k^2\binom{4k}{2k}}{(84-32\sqrt6)^{4k}} \left(280k+5\sqrt6+26\right)=\frac3π(2\sqrt3+33\sqrt2) \end{equation*} and \begin{align*}&\sum_{k=1}^\infty\frac{(27(37102-15147\sqrt6))^k}{k^3\binom{2k}k^2\binom{3k}k} \left(9k(11\sqrt6+51)-2(19\sqrt6+54)\right) \\&\qquad=\frac{5625}2\left(\sqrt6 L_{-24}(2)-3G\r…

This https://arxiv.org/abs/2411.17098 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Determination of the binding and $DK$ probability of the $D^{*}_{s0}(2317)$ from the $(\bar{D}\bar K)^-$ mass distributions in $Λ_{b}\to Λ_{c} (\bar{D}\bar K)^-$ decays
We study the $Λ_{b}\toΛ_{c}\bar{D}^{0}K^{-}$ and $Λ_{b}\to Λ_{c}D^{-}\bar{K}^{0}$ decays which proceed via a Cabibbo and $N_c$ favored process of external emission, and we determine the $\bar{D}^{0}K^{-}$ and $D^{-}\bar{K}^{0}$ mass distributions close to the $\bar{D} \bar{K}$ threshold. For this, we use the tree level contribution plus the rescattering of the meson-meson components, using the extension of the local hidden gauge approach to the charm sector that produces the $D^*_{s0}(2317)…

This https://arxiv.org/abs/2505.13168 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Knots that share four surgeries
Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct knots K,K' that have common Dehn surgeries for four distinct slopes. We also construct non-isotopic Legendrian knots K,K' that have contactomorphic contact (+1)-and (-1)-surgeries, disproving an analogous conjecture in contact geometry.

On Minimizers of Minimum Density
Arseny Shur
https://arxiv.org/abs/2506.05277 https://arxiv.org/pdf/2506.05277

On Minimizers of Minimum Density
Minimizers are sampling schemes with numerous applications in computational biology. Assuming a fixed alphabet of size $σ$, a minimizer is defined by two integers $k,w\ge2$ and a linear order $ρ$ on strings of length $k$ (also called $k$-mers). A string is processed by a sliding window algorithm that chooses, in each window of length $w+k-1$, its minimal $k$-mer with respect to $ρ$. A key characteristic of the minimizer is its density, which is the expected frequency of chosen $k$-mers among…

Measurement of the branching fractions of the Cabibbo-favored decays $\Lambda_{c}^{ }\to\Lambda K_{S}^{0}K^{ }$ and $\Lambda_{c}^{ }\to\Xi^{0}K_{S}^{0}\pi^{ }$ and search for $\Lambda_{c}^{ }\to\Sigma^{0} K_{S}^{0}K^{ }$
BESIII Collaboration, et al.
https://arxiv.org/abs/2506.02969

Measurement of the branching fractions of the Cabibbo-favored decays $Λ_{c}^{+}\toΛK_{S}^{0}K^{+}$ and $Λ_{c}^{+}\toΞ^{0}K_{S}^{0}π^{+}$ and search for $Λ_{c}^{+}\toΣ^{0} K_{S}^{0}K^{+}$
Based on $e^{+}e^{-}$ collision data corresponding to an integrated luminosity of about 4.5 fb$^{-1}$ collected at center-of-mass energies between 4599.53 MeV and 4698.82 MeV with the BESIII detector, the absolute branching fraction of the Cabibbo-favored decay $Λ_{c}^{+}\toΛK_{S}^{0}K^{+}$ is measured to be $(3.12\pm0.46\pm0.15)\times10^{-3}$. Combined with a previous measurement from the BESIII Collaboration, the branching fraction of the decay $Λ_{c}^{+}\toΛK_{S}^{0}K^{+}$ is calculated …

This https://arxiv.org/abs/2404.11841 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

On the Unprovability of Circuit Size Bounds in Intuitionistic $\mathsf{S}^1_2$
We show that there is a constant $k$ such that Buss's intuitionistic theory $\mathsf{IS}^1_2$ does not prove that SAT requires co-nondeterministic circuits of size at least $n^k$. To our knowledge, this is the first unconditional unprovability result in bounded arithmetic in the context of worst-case fixed-polynomial size circuit lower bounds. We complement this result by showing that the upper bound $\mathsf{NP} \subseteq \mathsf{coNSIZE}[n^k]$ is unprovable in $\mathsf{IS}^1_2$. In order to…

Homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$ in positive characteristic
Ryuji Tanimoto
https://arxiv.org/abs/2506.00423 https://

Homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$ in positive characteristic
Let $k$ be an algebraically closed field of positive characteistic $p$ and let ${\rm SL}(n, k)$ denote the special linear algebraic group of degree $n$ over $k$. In this paper, we describe homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$. As by-products of this description, we give a classification of homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$ and describe the indecomposable decompositions of homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$.

Cohen-Macaulay modules of covariants for cyclic $p$-groups
Jonathan Elmer
https://arxiv.org/abs/2506.03677 https://arxiv.org/pdf/2506…

Cohen-Macaulay modules of covariants for cyclic $p$-groups
Let $G$ be a a finite group, $k$ a field of characteristic dividing $|G|$ and and $V,W$ $kG$-modules. Broer and Chuai showed that if $\mathrm{codim}(V^G) \leq 2$ then the module of covariants $k[V,W]^G = (k[V]\otimes W)^G$ is a Cohen-Macaulay module, hence free over a homogeneous system of parameters for the invariant ring $k[V]^G$. In the present article we prove a general result which allows us to determine whether a set of elements of a free $A$-module is a generating set, for any …

Been there, done that: NATÜRLICH habe ich in #København auch #Pølser gegessen. Soll ja keiner merken, dass ich Tourist bin.
#food

On the sum of a prime and two Fibonacci numbers
Ji-Zhen Xu, Yong-Gao Chen
https://arxiv.org/abs/2506.03631 https://arxiv.org/pdf/2506…

On the sum of a prime and two Fibonacci numbers
Let $\{f_n\}$ be the Fibonacci sequence. For any positive integer $n$, let $r(n)$ be the number of solutions of $n=p+f_{k_1^{2}} +f_{k_{2}^{2}}$, where $p$ is a prime and $k_1, k_2$ are nonnegative integers with $k_1\le k_2$. In this paper, it is proved that $\{ n : r(n)=0\} $ contains an infinite arithmetic progression, and both sets $\{ n : r(n)=1\} $ and $\{ n : r(n)\ge 2\}$ have positive asymptotic densities.

This https://arxiv.org/abs/2312.00885 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Divisible minimal codes
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$ is denoted by $m(k,q)$. Here we determine $m(7,2)$, $m(8,2)$, and $m(9,2)$, as well as full classifications of all codes attaining $m(k,2)$ for $k\le 7$ and those attaining $m(9,2)$. We give improved upper bounds for $m(k,2)$ for all $10\le k\le 17$. It turn…

Pivoting the paradigm: the role of spreadsheets in K-12 data science
Oren Tirschwell, Nicholas Jon Horton
https://arxiv.org/abs/2506.03232 https://

Pivoting the paradigm: the role of spreadsheets in K-12 data science
Spreadsheet tools are widely accessible to and commonly used by K-12 students and teachers. They have an important role in data collection and organization. Beyond data organization, spreadsheets also make data visible and easy to interact with, facilitating student engagement in data exploration and analysis. Though not suitable for all circumstances, spreadsheets can and do help foster data and computing skills for K-12 students. This paper 1) reviews prior frameworks on K-12 data tools; 2) p…

Broncos meeting with former Ravens, Chargers RB J.K. Dobbins, per report

https://www.cbssports.com/nfl/news/broncos-meeting-with-former-ravens-charge…

This https://arxiv.org/abs/2206.05492 has been replaced.
link: https://scholar.google.com/scholar?q=a

Varieties of Nodal surfaces, coding theory and Discriminants of cubic hypersurfaces. Part 1: Generalities and nodal K3 surfaces. Part 2: Cubic Hypersurfaces, associated discriminants. Part 3: Nodal quintics. Part 4: Nodal sextics
We attach two binary codes to a projective nodal surface (the strict code K and, for even degree d, the extended code K' ) to investigate the `Nodal Severi varieties F(d, n) of nodal surfaces in P^3 of degree d and with n nodes, and their incidence hierarchy, relating partial smoothings to code shortenings. Our first main result solves a question which dates back over 100 years: the irreducible components of F(4, n) are in bijection with the isomorphism classes of their extended codes K', and t…

Auto verkauft ohne Papiere!? 🤔 #Polizeiruf110

The UK's FCA plans to lift its ban on offering crypto exchange traded notes to retail investors "to support UK growth and competitiveness" (Ian Allison/CoinDesk)
https://www.coindesk.com/policy/2025/06/06/uk…

This https://arxiv.org/abs/2506.00521 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence rates of regularized quasi-Newton methods without strong convexity
In this paper, we study convergence rates of the cubic regularized proximal quasi-Newton method (\csr) for solving non-smooth additive composite problems that satisfy the so-called Kurdyka-Łojasiewicz (KŁ) property with respect to some desingularization function $ϕ$ rather than strong convexity. After a number of iterations $k_0$, \csr\ exhibits non-asymptotic explicit super-linear convergence rates for any $k\geq k_0$. In particular, when $ϕ(t)=ct^{1/2}$, Cubic SR1 PQN has a convergence ra…

This https://arxiv.org/abs/2503.03076 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework
We present a new avenue of the Raychaudhuri Equation (RE) by introducing a non-affine parametrization within the k-essence framework. This modification accounts for non-geodesic flow curves, leading to emergent repulsive effects in cosmic evolution. Using a DBI-type k-essence Lagrangian, we derive a modified RE and demonstrate its ability to address the Hubble tension while predicting a natural emergence of a dynamical dark energy equation of state. Our Bayesian analysis, constrained by cosmolo…

You might want to fine-tune your notification settings:
“Apple Gave Governments Data on Thousands of Push Notifications” - https://www.404media.co/apple-gave-governments-data-on-thousands-of-push-notifications/

Apple Gave Governments Data on Thousands of Push Notifications
Push notification data can sometimes include the unencrypted content of notifications. Requests include from the U.S., U.K., Germany, and Israel.

Improving the average dilation of a metric graph by adding edges
Sariel Har-Peled, Eliot W. Robson
https://arxiv.org/abs/2506.04246 https://

Improving the average dilation of a metric graph by adding edges
For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to augment $G$ with $k$ additional edges to reduce the maximum dilation. In this note, we consider a variant of this problem where the goal is to reduce the average dilation for pairs of points in $G$. We provide an $O(k)$ approximation algorithm for this proble…

This https://arxiv.org/abs/2408.03465 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCC_…

Algorithms for the Diverse-k-SAT problem: the geometry of satisfying assignments
Given a $k$-CNF formula and an integer $s$, we study algorithms that obtain $s$ solutions to the formula that are maximally dispersed. For $s=2$, the problem of computing the diameter of a $k$-CNF formula was initiated by Creszenzi and Rossi, who showed strong hardness results even for $k=2$. Assuming SETH, the current best upper bound [Angelsmark and Thapper '04] goes to $4^n$ as $k \rightarrow \infty$. As our first result, we give exact algorithms for using the Fast Fourier Transform and cliq…

This https://arxiv.org/abs/2408.16243 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotically Compatible Error Bound of Finite Element Method for Nonlocal Diffusion Model with An Efficient Implementation
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes, the error is bounded by \(O(h^k + δ)\), where \(h\) is the mesh size, \(δ\) is the nonlocal horizon, and \(k\) is the order of the FEM basis. Without shape regularity, the bound becomes \(O(h^{k+1}/δ+ δ)\). In addition, we present an efficient implementati…

Hilarious Jon Stewart on the Mollusk #DOGE 😅 https://youtu.be/WIhlC3L99x8?si=K-R2z4kZGwHyZaqT

This https://arxiv.org/abs/2501.12729 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the algebraic transfers of ranks 4 and 6 at generic degrees
Let $\mathscr A$ denote the classical singly-graded Steenrod algebra over the binary field $\mathbb Z/2.$ We write $P_k:=\mathbb Z/2[t_1, t_2, \ldots, t_k]$ as the polynomial algebra on $k$ generators, each having a degree of one. Let $GL_k$ be the general linear group of rank $k$ over $\mathbb Z/2.$ Then, $P_k$ is an $ \mathscr A[GL_k]$-module. The structure of the cohomology groups, ${\rm Ext}_{ \mathscr A}^{k, k+\bullet}(\mathbb Z/2, \mathbb Z/2)$, of the Steenrod algebra has, thus far, resi…

Remove k emails from FriendFeed, linkedin, Google analytics that were sitting in mu gmail account from

This https://arxiv.org/abs/2501.09567 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
We employ the $\mathrm{SU}(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the $\mathrm{SU}(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau. It is demonstrated that the wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states such that many physical properties c…

This https://arxiv.org/abs/2407.10026 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Conditional Entropies of k-Deletion/Insertion Channels
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work is to study these entropy values for the k-deletion, k-insertion channels, where exactly k symbols are deleted, inserted in the transmitted sequence, respectively. If all possible sequences are transmitted with the same probability then studying the input and …

The Minkowski problem for the $k$-torsional rigidity
Xia Zhao, Peibiao Zhao
https://arxiv.org/abs/2505.24494 https://arxiv.org/pdf/25…

The Minkowski problem for the $k$-torsional rigidity
P. Salani [Adv. Math., 229 (2012)] introduced the $k$-torsional rigidity associated with a $k$-Hessian equation and obtained the Brunn-Minkowski inequalities $w.r.t.$ the torsional rigidity in $\mathbb{R}^3$. Following this work, we first construct, in the present paper, a Hadamard variational formula for the $k$-torsional rigidity with $1\leq k\leq n-1$, then we can deduce a $k$-torsional measure from the Hadamard variational formula. Based on the $k$-torsional measure, we propose the Minkowsk…

This https://arxiv.org/abs/2407.19004 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Weighing The Options: The Unseen Companion in LAMOST J2354 is Likely a Massive White Dwarf
LAMOST J235456.73+335625 (J2354) is a binary system hosting a $\sim 0.7~\rm M_\odot$ K dwarf and a $\sim 1.4~\rm M_\odot$ dark companion, supposedly a neutron star, in a 0.48d orbit. Here we present high- and low-resolution spectroscopy to better constrain the properties of the system. The low-resolution spectrum confirms that the luminous star is a slightly metal-poor K dwarf and strengthens the limits on any optical flux from the dimmer companion. We use the high-resolution spectra to measure…

Non-adiabatically driven quantum interference effects in the ultracold K KRb $\longrightarrow$ Rb K$_{2}$ chemical reaction
H. da Silva Jr., B. K. Kendrick, H. Li, S. Kotochigova, N. Balakrishnan
https://arxiv.org/abs/2506.01831

Non-adiabatically driven quantum interference effects in the ultracold K + KRb $\longrightarrow$ Rb + K$_{2}$ chemical reaction
The K + KRb $\longrightarrow$ Rb + K$_{2}$ chemical reaction is the first ultracold atom-diatom chemical reaction for which experimental results have been reported for temperatures below 1 $μ$K more than a decade ago. The reaction occurs through coupling with an excited electronic state that is accessible even in the ultracold limit. A previous quantum dynamics study, excluding non-adiabatic effects, has reported a rate coefficient that is about 35\% below the experimental value. Here, we repo…

On some semidirect products of skew braces arising in Hopf-Galois theory
Paul J. Truman
https://arxiv.org/abs/2506.04928 https://arxi…

On some semidirect products of skew braces arising in Hopf-Galois theory
We classify skew braces that are the semidirect product of an ideal and a left ideal. As a consequence, given a Galois extension of fields $ L/K $ whose Galois group is the semidirect product of a normal subgroup $ A $ and a subgroup $ B $, we classify the Hopf-Galois structures on $ L/K $ that realize $ L^{A} $ via a normal Hopf subalgebra and $ L^{B} $ via a Hopf subalgebra. We show that the Hopf algebra giving such a Hopf-Galois structure is the smash product of these Hopf subalgebras, and u…

Trump admits rupture with Musk: "Elon and I had a great relationship" (Avery Lotz/Axios)
https://www.axios.com/2025/06/05/trump-musk-bill-criticism-response
http://www.memeorandum.com/250605/p70#a250605p70

SHADOW OF INTENT - Mechanical Chaos (Official Music Video) | #NowPlaying

Mein Vortrag für die Tübix wurde angenommen:
Wie uns LLMs beim Programmieren helfen
#LLM

Graphene Electro-Absorption Modulators for Energy-Efficient and High-Speed Optical Transceivers
M. Tiberi, A. Montanaro, C. Wen, J. Zhang, O. Balci, S. M. Shinde, S. Sharma, A. Meersha, H. Shekhar, J. E. Muench, B. R. Conran, K. B. K. Teo, M. Ebert, X. Yan, Y. Tran, M. Banakar, C. Littlejohns, G. T. Reed, M. Romagnoli, A. Ruocco, V. Sorianello, A. C. Ferrari

Graphene Electro-Absorption Modulators for Energy-Efficient and High-Speed Optical Transceivers
The increasing demand for energy-efficient hardware for artificial intelligence (AI) and data centres requires integrated photonic solutions delivering optical transceivers with Tbit/s data rates and energy consumption$<$1pJ/bit. Here, we report double single-layer graphene electro-absorption modulators on Si optimized for energy-efficient and ultra-fast operation, demonstrating 67GHz bandwidth and 80Gbit/s data rate, in both O and C bands, using a fabrication tailored for wafer-scale integrati…

K-order Ranking Preference Optimization for Large Language Models
Shihao Cai, Chongming Gao, Yang Zhang, Wentao Shi, Jizhi Zhang, Keqin Bao, Qifan Wang, Fuli Feng
https://arxiv.org/abs/2506.00441

K-order Ranking Preference Optimization for Large Language Models
To adapt large language models (LLMs) to ranking tasks, existing list-wise methods, represented by list-wise Direct Preference Optimization (DPO), focus on optimizing partial-order or full-order list ranking consistency for LLMs to enhance their ranking abilities. However, we argue that optimizing top-K ranking consistency could be more appropriate for real-world applications. There are two main reasons: (1) users are typically concerned with only the top-K results, making top-K ranking more im…

Changing Look AGN: A study of Optical/UV and the Highly Ionized Fe K$\alpha$ X-ray Line Flux Variations Using Photo-Ionization Simulations
Tek P. Adhikari, Santanu Mondal, Zhicheng He, Agata Rozanska, Krzysztof Hryniewicz
https://arxiv.org/abs/2506.03540

Changing Look AGN: A study of Optical/UV and the Highly Ionized Fe K$α$ X-ray Line Flux Variations Using Photo-Ionization Simulations
Significant variability in broad emission line strengths of active galactic nuclei (AGN) over months to years has been observed, often accompanied by intrinsic continuum changes. Such spectral variability challenges the traditional AGN classification scheme, which attributes differences between Type 1 and Type 2 to geometrical effects, as transitions between these types occur on timescales shorter than viscous ones. In this work, using the {\sc cloudy} photo-ionization simulations, we investiga…

This https://arxiv.org/abs/2410.02544 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDC_…

Federated k-Core Decomposition: A Secure Distributed Approach
As one of the most well-studied cohesive subgraph models, the $k$-core is widely used to find graph nodes that are ``central'' or ``important'' in many applications, such as biological networks, social networks, ecological networks, and financial networks. For Decentralized Online Social Networks (DOSNs), where each vertex is a client as a single computing unit, distributed k-core decomposition algorithms have already been proposed. However, current distributed approaches fail to adequately pro…

1975: MUSIC, MUSAK and your MIND | Horizon: The Three Chord Trick |
https://youtube.com/watch?v=LkgNP5GWE-k&si=4ieR3ITQlWWXRdg2

🇺🇦 #NowPlaying on BBCRadio3's #ClassicalLive
Wolfgang Amadeus Mozart, Christiane Karg, Leif Aruhn-Solén, Jóhann Kristinsson, Danish National Concert Choir, Danish National Symphony Orchestra & Manfred Honeck:
🎵 Mass in C minor, K. 427
#WolfgangAmadeusMozart

Bei den #Kritzelspielen ging es heute zufällig um #Käse. Zufällig. Denn während der Planung wies jemand Marianne und Katrin darauf hin, dass der 4. Juni der Tag des Käses ist.
Das ist mein Ergebnis, daran hab ich nun aber auch einige Zeit „rumgemalt!“

Bei den #Kritzelspielen ging es heute zufällig um #Käse. Zufällig. Denn während der Planung wies jemand Marianne und Katrin darauf hin, dass der 4. Juni der Tag des Käses ist.
Das ist mein Ergebnis, daran hab ich nun aber auch einige Zeit „rumgemalt!“

Such a principled, stand-up guy. I am considering going back to X to help the cause ->
Trump-Musk row explodes as billionaire claims President named in Epstein files | BBC News - BBC News
https://www.youtube.com/watch?v=8vg2D3Pi9Rk

Some series connecting Fibonacci numbers to $\pi$
Zhi-Wei Sun, Yajun Zhou
https://arxiv.org/abs/2506.01865 https://arxiv.org/pdf/2506…

Some series connecting Fibonacci numbers to $π$
In this paper, we mainly deduce several series identities connecting the Fibonacci numbers to $π$. For example, we prove that \[\sum_{k=1}^{\infty}\frac{(135 k-56) F_{8 k}-2 (105 k-44) F_{8 k-1}}{k^{3}\binom{2k}{k}^3}=\frac{7π^{2}}{3}\]and\[\sum_{k=0}^\infty\frac{\binom{2k}{k}^3}{2^{12k}}\big[ 2 (90 k+13) F_{8 k}-2 (30 k-1) F_{8 k-1}\big]=\frac{64}π.\]

This https://arxiv.org/abs/2505.09400 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Structured coalescents, coagulation equations and multi-type branching processes
Consider a structured population consisting of $d$ colonies, with migration rates that are proportional to a positive parameter $K$. We sample $N_K$ individuals distributed evenly across the $d$ colonies and trace their ancestral lineages back. Within a colony, we assume that pairs of ancestral lineages coalesce at a constant rate, as in a Kingman's coalescent. We identify each ancestral lineage with the set, or block, of its descendants in the sample and we encode the state of the system using…

🇺🇦 #NowPlaying on KEXP's #MiddayShow
The Clientele:
🎵 Since K Got Over Me
#TheClientele
https://theclientele.bandcamp.com/track/since-k-got-over-me
https://open.spotify.com/track/0N0BwroI7zvuzVhIai2esX

The random $k$-SAT Gibbs uniqueness threshold revisited
Arnab Chatterjee, Amin Coja-Oghlan, Catherine Greenhill, Vincent Pfenninger, Maurice Rolvien, Pavel Zakharov, Kostas Zampetakis
https://arxiv.org/abs/2506.01359

The random $k$-SAT Gibbs uniqueness threshold revisited
We prove that for any $k\geq3$ for clause/variable ratios up to the Gibbs uniqueness threshold of the corresponding Galton-Watson tree, the number of satisfying assignments of random $k$-SAT formulas is given by the `replica symmetric solution' predicted by physics methods [Monasson, Zecchina: Phys. Rev. Lett. (1996)]. Furthermore, while the Gibbs uniqueness threshold is still not known precisely for any $k\geq3$, we derive new lower bounds on this threshold that improve over prior work [Montan…

Well-hued graphs with first difference two
Geoffrey Boyer, Kirsti Kuenzel, Jeremy Lyle, Ryan Pellico
https://arxiv.org/abs/2506.04993 https://

Well-hued graphs with first difference two
A graph $G$ is said to be well-hued if every maximal $k$-colorable subgraph of $G$ has the same order $a_k$. Therefore, if $G$ is well-hued, we can associate with $G$ a sequence $\{a_k\}$. Necessary and sufficient conditions were given as to when a sequence $\{a_k\}$ is realized by a well-hued graph. Further, it was conjectured there is only one connected well-hued graph with $a_2 = a_1 + 2$ for every $a_1 \ge 4$. In this paper, we prove this conjecture as well as characterize nearly all well-h…

This https://arxiv.org/abs/2505.22984 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

A Computational Approach to Improving Fairness in K-means Clustering
The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some sensitive variable, e.g., gender or race. Such a fairness issue may cause bias and unexpected social consequences. This work attempts to improve the fairness of K-means clustering with a two-stage optimization formulation--clustering first and then adjust cluster …

An der Regie ist heute nichts auszusetzen 👍🏻 #Polizeiruf110

Resilient Pattern Mining
Pengxin Bian, Panagiotis Charalampopoulos, Lorraine A. K. Ayad, Manal Mohamed, Solon P. Pissis, Grigorios Loukides
https://arxiv.org/abs/2506.04935

Resilient Pattern Mining
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $τ$ times in $S$, for some integer $τ\in[1,n]$. We introduce a resilient version of this classic problem, which we term the $(τ, k)$-Resilient Pattern Mining (RPM) problem. Given a string $S$ of length $n$ and two integers $τ, k\in[1,n]$, RPM asks for the set of substrings of $S$ that occur at least $τ$ times in $S$,…

On the domination of surface-group representations in $\mathrm{PU}(2,1)$
Pabitra Barman, Krishnendu Gongopadhyay
https://arxiv.org/abs/2506.03838 https://

On the domination of surface-group representations in $\mathrm{PU}(2,1)$
This article explores surface-group representations into the complex hyperbolic group $\mathrm{PU}(2,1)$ and presents domination results for a special class of representations called $T$-bent representations. Let $S_{g,k}$ be a punctured surface of negative Euler characteristic. We prove that for a $T$-bent representation $ρ: π_1(S_{g,k}) \rightarrow \mathrm{PU}(2,1)$, there exists a discrete and faithful representation $ρ_0: π_1(S_{g,k}) \rightarrow \mathrm{PO}(2,1)$ that dominates $ρ$ in…

Apple's July 2022 to June 2024 transparency report shows it gave governments data on thousands of push notifications, which can include unencrypted content (Joseph Cox/404 Media)
https://www.404media.co/apple-gave-governments-data-on-tho…

Apple Gave Governments Data on Thousands of Push Notifications
Push notification data can sometimes include the unencrypted content of notifications. Requests include from the U.S., U.K., Germany, and Israel.

This https://arxiv.org/abs/2410.04348 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Explaining the $B_{d(s)} \rightarrow K^{(\ast)}\bar{K}^{(\ast)}$ puzzle via chiral-flip in $R$-parity violating MSSM with seesaw mechanism
We study the non-leptonic puzzle of $B_{d(s)} \rightarrow K^{(\ast)}\bar{K}^{(\ast)}$ decay in the $R$-parity violating minimal supersymmetric standard model (RPV-MSSM) extended with the inverse seesaw mechanism. In this model, the chiral flip of sneutrinos can contribute to the observables $L_{K\bar{K}}$ and $L_{K^{\ast}\bar{K}^{\ast}}$, that is benefit for explaining the relevant puzzle. We also find that this unique effect can engage in the $B_s$-$\bar{B}_s$ mixing. We utilize the scenario o…

This https://arxiv.org/abs/2405.10533 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Anticanonical minimal models and Zariski decomposition
Birkar and Hu showed that if a pair $(X,Δ)$ is lc and $K_{X}+Δ$ admits a birational Zariski decomposition, then $(X,Δ)$ has a minimal model. Analogously, we prove that if a pair $(X,Δ)$ is pklt and $-(K_{X}+Δ)$ admits a birational Zariski decomposition, then $(X,Δ)$ has an anticanonical minimal

This https://arxiv.org/abs/2503.09920 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Black-bounce solutions in a k-essence theory under the effects of bumblebee gravity
In the present study, we analyze the effects of violation of Lorentz symmetry for black-bounce solutions in a $k$-essence theory that has the form of a power law for the configuration $n=1/3$. We perform such analysis for a known model explored in previous work $Σ^2=x^2+a^2$ and complement the proposal with a new black-bounce model for the area functions $Σ^2_1=\sqrt{x^4+d^4}$. This model has the Schwarzschild-de Sitter asymptomatic behavior for $x\to{-\infty}$, and we investigate the scalar …

Ikea ist überall #Polizeiruf110

Bounded powers of edge ideals: The strong exchange property
Takayuki Hibi, Seyed Amin Seyed Fakhari
https://arxiv.org/abs/2506.03480 https://

Bounded powers of edge ideals: The strong exchange property
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $\mathfrak{c}\in\mathbb{Z}_{>0}^n$, the ideal $I_{\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\mathfrak{c}$. Let $δ_{\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\mathfrak{c}}\neq 0$. Let $I(G) \subset S$ denote the edge ideal of a finite graph $G$ on …

This https://arxiv.org/abs/2407.08438 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Symmetries of power-free integers in number fields and their shift spaces
We describe the group of $\mathbb Z$-linear automorphisms of the ring of integers of a number field $K$ that preserve the set $V_{K,k}$ of $k$th power-free integers: every such map is the composition of a field automorphism and the multiplication by a unit. We show that those maps together with translations generate the extended symmetry group of the shift space $\mathbb D_{K,k}$ associated to $V_{K,k}$. Moreover, we show that no two such dynamical systems $\mathbb D_{K,k}$ and $\mathbb D_{L,…

Frobenius theorem and fine structure of tangency sets to non-involutive distributions
Giovanni Alberti, Annalisa Massaccesi, Andrea Merlo
https://arxiv.org/abs/2506.03715

Frobenius theorem and fine structure of tangency sets to non-involutive distributions
In this paper we provide a complete answer to the question whether Frobenius' Theorem can be generalized to surfaces below the $C^{1,1}$ threshold. We study the fine structure of the tangency set in terms of involutivity of a given distribution and we highlight a tradeoff behavior between the regularity of a tangent surface and that of the tangency set. First of all, we prove a Frobenius-type result, that is, given a $k$-dimensional surface $S$ of class $C^1$ and a non-involutive $k$-distributi…

A first view on the density of 5-planar graphs
Aaron B\"ungener, Jakob Franz, Michael Kaufmann, Maximilian Pfister
https://arxiv.org/abs/2505.24364 ht…

A first view on the density of 5-planar graphs
$k$-planar graphs are generalizations of planar graphs that can be drawn in the plane with at most $k > 0$ crossings per edge. One of the central research questions of $k$-planarity is the maximum edge density, i.e., the maximum number of edges a $k$-planar graph on $n$ vertices may have. While there are numerous results for the classes of general $k$-planar graphs for $k\leq 2$, there are only very few results for increasing $k=3$ or $4$ due to the complexity of the classes. We make a first st…

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Imperial Teen:
🎵 Teacher's Pet
#ImperialTeen
https://imperialteen.bandcamp.com/track/teachers-pet
https://open.spotify.com/track/7HYXsAARjUvCAeLWJ3uZ2h

Das Kind ist aber warm angezogen zum Schlafen #Polizeiruf110

Free actions on products of real projective spaces
Ergun Yalcin
https://arxiv.org/abs/2506.04067 https://arxiv.org/pdf/2506.04067

Free actions on products of real projective spaces
We prove that if $G=(\mathbb{Z}/2)^r$ acts freely and cellularly on a finite-dimensional CW-complex $X$ homotopy equivalent to $\mathbb{R}P ^{n_1} \times \cdots \times \mathbb{R} P ^{n_k}$ with trivial action on the mod-$2$ cohomology, then $r \leq μ(n_1)+ \cdots + μ(n_k )$ where for each integer $n\geq 0$, $μ(n)=0$ if $n$ is even, $μ(n)=1$ if $n\equiv 1$ mod 4, and $μ(n)=2$ if $n\equiv 3$ mod 4. This proves a homotopy-theoretic version of a conjecture of Cusick.

Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$
Anna-Maria Raukh
https://arxiv.org/abs/2506.04094 https://

Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$
Given a hypersurface $i \colon X \hookrightarrow \widetilde{P}^n$ in a weighted projective space, we compute the intersection form on the second cohomology $H^2(X, \mathbb{Z})^{\otimes n-1} \to \mathbb{Z}$ for the purpose of identifying Fano manifolds obtained from smoothing singular Fanos. In the process, we describe the integer cohomology groups $H^k(X, \mathbb{Z})$ for $k

On the quadratic 8-edge case of the Brown-Erd\H{o}s-S\'os problem
Oleg Pikhurko, Shumin Sun
https://arxiv.org/abs/2506.01739 https://

On the quadratic 8-edge case of the Brown-Erdős-Sós problem
Let $f^{(r)}(n;s,k)$ be the maximum number of edges in an $n$-vertex $r$-uniform hypergraph containing no $k$ edges on at most $s$ vertices. Brown, Erdős and Sós conjectured in 1973 that the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(3)}(n;k+2,k)$ exists for all $k$. Recently, Delcourt and Postle settled the conjecture and their approach was generalised by Shangguan to every uniformity $r\ge 4$: the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(r)}(n;rk-2k+2,k)$ exists for all $r\ge 3$ and $k\ge…

This https://arxiv.org/abs/2506.02491 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

On the Inversion Modulo a Power of an Integer
Recently, Koc proposed a neat and efficient algorithm for computing $x = a^{-1} \pmod {p^k}$ for a prime $p$ based on the exact solution of linear equations using $p$-adic expansions. The algorithm requires only addition and right shift per step. In this paper, we design an algorithm that computes $x = a^{-1} \pmod {n^k}$ for any integer $n>1$. The algorithm has a motivation from the schoolbook multiplication and achieves both efficiency and generality. The greater flexibility of our algorithm …

This https://arxiv.org/abs/2411.13818 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Proof of Merca's stronger conjecture on truncated Jacobi triple product series
In the study of theta series and partition functions, Andrews and Merca, Guo and Zeng independently conjectured that a truncated Jacobi triple product series has nonnegative coefficients. This conjecture was proved analytically by Mao and combinatorially by Yee. In 2021, Merca proposed a stronger version of the conjecture, that is, for positive integers $1\leq S

Heißt "Wir haben vereinbart, dass du meine Schicht übernimmst", dass Sarah einfach anstelle der Mutter gearbeitet hat, also illegal 🤔 #Polizeiruf110

This https://arxiv.org/abs/2403.17490 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Reconstruction of hypersurfaces from their invariants
Let $K$ be a field of characteristic $0$. We present an explicit algorithm that, given the invariants of a generic homogeneous polynomial $f$ under the linear action of $\mathrm{GL}_n$ or $\mathrm{SL}_n$, returns a polynomial differing from $f$ only by a linear change of variables with coefficients in a finite extension of $K$. Our approach uses the theory of covariants and the Veronese embeddings to characterize the linear equivalence class of a homogeneous polynomial through equations whose c…

Gravitational Collapse: Generalizing Oppenheimer-Snyder and a Conjecture on Horizon Formation Time
H. Khodabakhshi, H. Lu, F. Shojai
https://arxiv.org/abs/2506.03702

Gravitational Collapse: Generalizing Oppenheimer-Snyder and a Conjecture on Horizon Formation Time
We generalize the Oppenheimer-Snyder model of gravitational collapse by considering a broader class of static, spherically symmetric exterior spacetimes, with an interior geometry described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. Using Painleve-Gullstrand (PG) coordinates for the spatially flat interior geometry (k=0) and a Novikov-like coordinate system for the spatially closed geometry (k=1), we ensured a smooth transition between the interior and exterior of the collapsing …

Relative uniform $K$-stability over models implies existence of extremal metrics
Yoshinori Hashimoto
https://arxiv.org/abs/2506.02360 https://

Relative uniform $K$-stability over models implies existence of extremal metrics
We prove that an extremal metric on a polarised smooth complex projective variety exists if it is $\mathbb{G}$-uniformly $K$-stable relative to the extremal torus over models, extending a result due to Chi Li for constant scalar curvature Kähler metrics.

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Magdalena Bay:
🎵 Image
#MagdalenaBay
https://magdalenabay.bandcamp.com/track/image-grimes-special
https://open.spotify.com/track/0QW0KPBXXv67haGjbtkRRB

Ich weiß es: Es muss der Red-Porsche-Killer gewesen sein #Polizeiruf110

Hypergraphs accumulate infinitely often
David Conlon, Bjarne Sch\"ulke
https://arxiv.org/abs/2506.03080 https://arxiv.org/pdf/25…

Hypergraphs accumulate infinitely often
We show that the set $Π^{(k)}$ of Turán densities of $k$-uniform hypergraphs has infinitely many accumulation points in $[0,1)$ for every $k \geq 3$. This extends an earlier result of ours showing that $Π^{(k)}$ has at least one such accumulation point.

Rumors on evolving graphs through stationary times
Vicenzo Bonasorte
https://arxiv.org/abs/2506.04386 https://arxiv.org/pdf/2506.0438…

Rumors on evolving graphs through stationary times
We study rumor spreading in dynamic random graphs. Starting with a single informed vertex, the information flows until it reaches all the vertices of the graph (completion), according to the following process. At each step $k$, the information is propagated to neighbors of the informed vertices, in the $k$-th generated random graph. The way this information propagates from vertex to vertex at each step will depend on the ``protocol". We provide a method based on strong stationary times to study…

An application of the hit problem to the algebraic transfer
Nguyen Sum
https://arxiv.org/abs/2505.23218 https://arxiv.org/pdf/2505.23…

An application of the hit problem to the algebraic transfer
Let $P_k$ be the polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_k]$ over the field $\mathbb F_2$ with two elements, in $k$ variables $x_1, x_2, \ldots , x_k$, each variable of degree 1. Denote by $GL_k$ the general linear group over $\mathbb F_2$ which regularly acts on $P_k$. The algebra $P_k$ is a module over the mod-2 Steenrod algebra $\mathcal A$. In 1989, Singer [22] defined the $k$-th homological algebraic transfer, which is a homomorphism $$φ_k=(φ_k)_m :{\rm Tor}^{\mathcal A}_{k,k+m…

On the homological shifts of cover ideals of Cohen-Macaulay graphs
Amit Roy, Kamalesh Saha
https://arxiv.org/abs/2506.01810 https://a…

On the homological shifts of cover ideals of Cohen-Macaulay graphs
For a non-negative integer $k$, let $\mathrm{HS}_{k}(J(G))$ denote the $k^{\text{th}}$ homological shift ideal of the vertex cover ideal $J(G)$ of a graph $G$. For each $k\geq 2$, we construct a Cohen-Macaulay very well-covered graph $G_k$ which is both Cohen-Macaulay bipartite and a whiskered graph so that $\mathrm{HS}_{k}(J(G))$ does not have a linear resolution. This contradicts several results as well as disproves a conjecture in [J. Algebra, $\mathbf{629}$, (2023), 76-108] and [Mediterr. J…

Poincar\'e series of valuations on functions over a field
Antonio Campillo, Felix Delgado, Sabir Gusein-Zade
https://arxiv.org/abs/2506.02693 https://

Poincaré series of valuations on functions over a field
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coeficients in $\K$. We compute the semigroup Poincaré series and the classical Poincaré series of a valuation.

Wenigstens wissen wir jetzt, wer es war – nur noch nicht was und warum und wie ein silberner Mercedes ins Spiel kommt #Polizeiruf110

Various irrational series involving binomial coefficients
Zhi-Wei Sun
https://arxiv.org/abs/2506.01870 https://arxiv.org/pdf/2506.018…

Various irrational series involving binomial coefficients
Motivated by Galois theory, we propose some new irrational series of Ramanujan's type or Zeilberger's type. For example, we conjecture that \begin{equation*}\sum_{k=1}^\infty\frac{\binom{2k}k^2\binom{4k}{2k}}{(84-32\sqrt6)^{4k}} \left(280k+5\sqrt6+26\right)=\frac3π(2\sqrt3+33\sqrt2) \end{equation*} and \begin{align*}&\sum_{k=1}^\infty\frac{(27(37102-15147\sqrt6))^k}{k^3\binom{2k}k^2\binom{3k}k} \left(9k(11\sqrt6+51)-2(19\sqrt6+54)\right) \\&\qquad=\frac{5625}2\left(\sqrt6 L_{-24}(2)-3G\r…

Girth and Laplacian eigenvalue distribution
Leyou Xu, Bo Zhou
https://arxiv.org/abs/2506.00921 https://arxiv.org/pdf/2506.00921

Girth and Laplacian eigenvalue distribution
Let $G$ be a connected graph of order $n$ with girth $g$. For $k=1,\dots,\min\{g-1, n-g\}$, let $n(G,k)$ be the number of Laplacian eigenvalues (counting multiplicities) of $G$ that fall inside the interval $[n-g-k+4,n]$. We prove that if $g\ge 4$, then \[ n(G,k)\le n-g. \] Those graphs achieving the bound for $k=1,2$ are determined. We also determine the graphs $G$ with $g=3$ such that $n(G,k)=n-1, n-2, n-3$.

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Kali Uchis:
🎵 In My Dreams
#KaliUchis
https://djyungsavage.bandcamp.com/track/in-my-dreams-yung-avage-mix
https://open.spotify.com/track/2dDzrUEDCKXaLViMPa1jo5

Heute muss man wieder damit klar kommen, dass Brocki plötzlich im #Polizeiruf110 ermittelt

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
Defa Chen, Zhenan Sui, Letao Sun
https://arxiv.org/abs/2506.00565 https://

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
We prove the existence of smooth complete $2$-convex hypersurface which satisfies prescribed curvature equation $(κ_1 + κ_2)(κ_1 + κ_3)(κ_2 + κ_3) = (2 σ)^3$ and has prescribed asymptotic boundary at infinity of hyperbolic space of dimension 4, where $σ\in (0, 1)$ is a constant. We also prove the existence for $σ_k (κ_2 + \cdots + κ_n, \cdots, κ_1 + \cdots + κ_{n - 1}) = C_n^k (n - 1)^k σ^k$ with $k < n$ in $\mathbb{H}^{n + 1}$.

On the number of divisors of Mersenne numbers
Vjekoslav Kova\v{c}, Florian Luca
https://arxiv.org/abs/2506.04883 https://arxiv.org/pd…

On the number of divisors of Mersenne numbers
Denote $f(n):=\sum_{1\le k\le n} τ(2^k-1)$, where $τ$ is the number of divisors function. Motivated by a question of Paul Erdős, we show that the sequence of ratios $f(2n)/f(n)$ is unbounded. We also present conditional results on the divergence of this sequence to infinity. Finally, we test numerically both the conjecture $f(2n)/f(n)\to\infty$ and our sufficient conditions for it to hold.

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Pedro the Lion:
🎵 Modesto
#PedrotheLion
https://pedrothelion.bandcamp.com/track/modesto-live-at-the-crumb
https://open.spotify.com/track/5rAd7McVKxDk1gS5eNo9bE

Some Bounds Related to the 2-adic Littlewood Conjecture
Dinis Vitorino, Ingrid Vukusic
https://arxiv.org/abs/2506.04110 https://arxiv…

Some Bounds Related to the 2-adic Littlewood Conjecture
For every irrational real $α$, let $M(α) = \sup_{n\geq 1} a_n(α)$ denote the largest partial quotient in its continued fraction expansion (or $\infty$, if unbounded). The $2$-adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational $α$ such that $M(2^k α)$ is uniformly bounded by a constant $C$ for all $k\geq 0$. Badziahin proved (considering a different formulation of 2LC) that if a counterexample exists, then the bound $C$ is at least $8$. We improve this bou…

Perfect $1$-factorisations of $K_{11,11}$
Jack Allsop, Ian M. Wanless
https://arxiv.org/abs/2506.02455 https://arxiv.org/pdf/2506.024…

Perfect $1$-factorisations of $K_{11,11}$
A perfect $1$-factorisation of a graph is a decomposition of that graph into $1$-factors such that the union of any two $1$-factors is a Hamiltonian cycle. A Latin square of order $n$ is row-Hamiltonian if for every pair $(r,s)$ of distinct rows, the permutation mapping $r$ to $s$ has a single cycle of length $n$. We report the results of a computer enumeration of the perfect $1$-factorisations of the complete bipartite graph $K_{11,11}$. This also allows us to find all row-Hamiltonian Latin sq…

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Adrian Younge:
🎵 Esperando por Voce
#AdrianYounge
https://adrianyounge.bandcamp.com/track/esperando-por-voc
https://open.spotify.com/track/3mrZEBBswON1Ewxt9LIl0r

On the maximum number of edges of outer k-planar graphs
Maximilian Pfister
https://arxiv.org/abs/2505.24490 https://arxiv.org/pdf/250…

On the maximum number of edges of outer k-planar graphs
We study the maximum number of straight-line segments connecting $n$ points in convex position in the plane, so that each segment intersects at most $k$ others. This question can also be framed as the maximum number of edges of an outer $k$-planar graph on $n$ vertices. We outline several approaches to tackle the problem with the best approach yielding an upper bound of $(\sqrt{2}+\varepsilon)\sqrt{k}n$ edges (with $\varepsilon \rightarrow 0$ for sufficiently large $k$). We further investigate …

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Adrian Younge:
🎵 Nos Somos as Estrelas
#AdrianYounge
https://adrianyounge.bandcamp.com/track/nos-somos-as-estrelas
https://open.spotify.com/track/2ZDKqRiU308DT1OTvnQg03

Multivariable period rings of $p$-adic false Tate curve extension
Yijun Yuan
https://arxiv.org/abs/2505.24064 https://arxiv.org/pdf/2…

Multivariable period rings of $p$-adic false Tate curve extension
Let $p\geq 3$ be a prime number and $K$ be a finite extension of $\mathbf{Q}_p$ with uniformizer $π_K$. In this article, we introduce two multivariable period rings $\mathbf{A}_{\mathfrak{F},K}^{\operatorname{np}}$ and $\mathbf{A}_{\mathfrak{F},K}^{\operatorname{np},\operatorname{c}}$ for the étale $(φ,Γ_{\mathfrak{F},K})$-modules of $p$-adic false Tate curve extension $K\left(π_K^{1/p^\infty},ζ_{p^\infty}\right)$. Various properties of these rings are studied and as applications, we show…

This https://arxiv.org/abs/2407.08881 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces
Consider $N \geq 1$, $k \geq 2$, and $χ$ a Dirichlet character modulo $N$ such that $χ(-1) = (-1)^k$. For any bound $B$, one can show that $\dim S_k(Γ_0(N),χ) \le B$ for only finitely many triples $(N,k,χ)$. It turns out that this property does not extend to the newspace; there exists an infinite family of triples $(N,k,χ)$ for which $\dim S_k^{\text{new}}(Γ_0(N),χ) = 0$. However, we classify this case entirely. We also show that excluding the infinite family for which $\dim S_k^{\text{…

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Mos Def:
🎵 Universal Magnetic
#MosDef
https://djmickeyknox.bandcamp.com/track/mos-def-universal-magnetic-prod-shawn-j-period
https://open.spotify.com/track/3SY3xz2g0a4zGrn0V8MUt9

This https://arxiv.org/abs/2003.11202 has been replaced.
link: https://scholar.google.com/scholar?q=a

Set System Blowups
We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at most $w$, a typical $k$-tuple of sets $(S_1, \cdots, S_k)$ from $\mathcal{F}$ can be ``blown up" in the following sense: for each $1 \le i \le k$, we can find a large subfamily $\mathcal{F}_i$ containing $S_i$ so that for $i \neq j$, if $T_i \in \mathcal{F}_i$ and $T_j \in \mathcal{F}_j$ , then $T_i \cap T_j=S_i \cap S_j$. We also show that the answer to the multicolor version of the sunflower conje…

Overgroups of the arboreal representation of PCF polynomial
Wayne Peng
https://arxiv.org/abs/2506.00456 https://arxiv.org/pdf/2506.00…

Overgroups of the arboreal representation of PCF polynomial
Consider a number field $K$ and a rational function $f$ of degree greater than 1 over $K$. By taking preimages of $α\in K$ under successive iterates of $f$, an infinite $d$-ary tree $T_\infty$ rooted at $α$ can be constructed. An edge is assigned between two preimages $x$ and $y$ if $f(x)=y$. The absolute Galois group of $K$, acting on $T_\infty$ through tree automorphisms, generates a subgroup $\text{Gal}_f^\infty(α)$ in the group of all automorphisms of $T_\infty$, $\text{Aut}(T_\infty)$. …