Tootfinder

A note on some spectral properties of generalised pancake graphs
Gary R. W. Greaves, Haoran Zhu
https://arxiv.org/abs/2509.09425 https://arxiv.org/pdf/2509…

A note on some spectral properties of generalised pancake graphs
We prove that the spectral gap of generalised pancake graphs is strictly less than 2 and strictly less than 1 for burnt pancake graphs. In addition, we establish lower bounds on the multiplicities of certain integer eigenvalues of generalised pancake graphs. Together, these results settle two recent conjectures of Blanco and Buehrle.

Arithmetic properties of partition functions introduced by Pushpa and Vasuki
Hemjyoti Nath, Manjil P. Saikia
https://arxiv.org/abs/2509.08801 https://arxiv…

Arithmetic properties of partition functions introduced by Pushpa and Vasuki
In this short note, we prove several infinite family of congruences for some restricted partitions introduced by Pushpa and Vasuki (2022) (thereby, also proving a conjecture of Dasappa et. al. (2023)). We also prove some isolated congruences which seem to have been missed by earlier authors. Our proof techniques uses both elementary means as well as the theory of modular forms.

Some remarks on decay in countable groups and amalgamated free products
Srivatsav Kunnawalkam Elayavalli, Gregory Patchell, Lizzy Teryoshin
https://arxiv.org/abs/2509.08754 http…

Some remarks on decay in countable groups and amalgamated free products
In this note, we first study the notion of subexponential decay (SD) for countable groups with respect to a length function, which generalizes the well-known rapid decay (RD) property, first discovered by Haagerup in 1979. Several natural properties and examples are studied, especially including groups that have SD, but not RD. This consideration naturally has applications in $C^*$-algebras. We also consider in this setting a permanence theorem for decay in amalgamated free products (proved als…

A Note on Persistence Theory with Applications
N. Pant (University of Louisiana at Lafayette)
https://arxiv.org/abs/2509.06135 https://arxiv.org/pdf/2509.0…

A Note on Persistence Theory with Applications
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a roadmap to show the persitence of dynamical systems by discussing some problems from literature, which mainly involves either dealing with spectral radius or the Lyapunov exponents.

A Brief Note on Cryptographic Pseudonyms for Anonymous Credentials
Ren\'e Mayrhofer, Anja Lehmann, abhi shelat
https://arxiv.org/abs/2510.05419 https://

A Brief Note on Cryptographic Pseudonyms for Anonymous Credentials
This paper describes pseudonyms for the upcoming European Identity Wallet (EUDIW) architecture from both a cryptographic and an implementation perspective. Its main goal is to provide technical insights into the achievable properties and cryptographic realizations. In particular, we (1) outline the security and privacy requirements of EUDI pseudonyms as the basis for building consensus on the cross-country decision maker level; (2) sketch an abstract cryptographic protocol that fulfills these r…

Mean and quantile regression in the copula setting: properties, sharp bounds and a note on estimation
Henrik Kaiser, Wolfgang Trutschnig
https://arxiv.org/abs/2510.03804 https:/…

Mean and quantile regression in the copula setting: properties, sharp bounds and a note on estimation
Driven by the interest on how uniformity of marginal distributions propa\-gates to properties of regression functions, in this contribution we tackle the following questions: Given a $(d-1)$-dimensional random vector $\textbf{X}$ and a random variable $Y$ such that all univariate marginals of $(\textbf{X},Y)$ are uniformly distributed on $[0,1]$, how large can the average absolute deviation of the mean and the quantile regression function of $Y$ given $\textbf{X}$ from the value $\frac{1}{2}$ b…

Frame properties induced by iteration of a multiplication operator on Hardy spaces
Jahangir Cheshmavar
https://arxiv.org/abs/2509.04879 https://arxiv.org/p…

Frame properties induced by iteration of a multiplication operator on Hardy spaces
Motivated by the study of frame properties arising from iterates of linear operators, it was previously established that the multiplication operator $T_ϕx(t) = ϕ(t)x(t)$ cannot generate a frame in $L^2(a,b)$ (Results Math, 2019). In this note, we examine the behavior of such operators on the Hardy space $H^2(D)$, the Hilbert space of holomorphic functions on the open unit disk $D$ with square integrable boundary values. We show that, in contrast to the $L^2$-setting, the iterates of $T_ϕ$, f…

Splittings of Ideals of Points in $\mathbb{P}^{1}\times\mathbb{P}^{1}$
Elena Guardo, Graham Keiper, Adam Van Tuyl
https://arxiv.org/abs/2510.05628 https://…

Splittings of Ideals of Points in $\mathbb{P}^{1}\times\mathbb{P}^{1}$
Let $I_\mathbb{X}$ be the bihomogeneous ideal of a finite set of points $\mathbb{X} \subseteq \mathbb{P}^1 \times \mathbb{P}^1$. The purpose of this note is to consider ``splittings'' of the ideal $I_\mathbb{X}$, that is, finding ideals $J$ and $K$ such that $I_\mathbb{X} = J+K$, where $J$ and $K$ have prescribed algebraic or geometric properties. We show that for any set of points $\mathbb{X}$, we cannot partition the generators of $I_\mathbb{X}$ into two ideals of points. The best case scenar…

A note on maximal operators for moment curves
Chenjian Wang
https://arxiv.org/abs/2509.01173 https://arxiv.org/pdf/2509.01173

A note on maximal operators for moment curves
We consider a type of maximal operators associated to moment curves in $\mathbb R^d, d\geq 3.$ We derive $L^p$ mapping properties for these operators. In a special case, the estimate is sharp.

Non-fibered strongly quasipositive links and tightness
Isacco Nonino, Miguel Orbegozo Rodriguez
https://arxiv.org/abs/2509.26183 https://arxiv.org/pdf/2509…

Non-fibered strongly quasipositive links and tightness
It is well known that for fibered links in $\mathbb{S}^3$ being strongly quasipositive and supporting a tight contact structure are equivalent notions (arXiv:math/0509499). In this note we analyze the relation between these two properties for non fibered links. A non fibered link (together with an incompressible Seifert surface) induces a natural partial open book (arXiv:2509.09615). We prove that strongly quasipositive links induce tight contact structures. We also show that, in contrast to th…

Local newforms for generic representations of $p$-adic ${\rm SO}_{2n 1}$: Uniqueness
Yao Cheng
https://arxiv.org/abs/2510.03068 https://arxiv.org/pdf/2510.…

Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness
The conjectural theory of local newofmrs for the split $p$-adic group ${\rm SO}_{2n+1}$, proposed by Gross, predicts that the space of local newforms in a generic representation is one-dimensional. In this note, we prove that this space is at most one-dimensional and verify its expected arithmetic properties, conditional on existence. These results play an important role in our proof of the existence part of the newform conjecture.

The Large Magellanic Cloud as a source of the highest energy cosmic rays
Roger Clay, Tadeusz Wibig
https://arxiv.org/abs/2507.16378 https://

The Large Magellanic Cloud as a source of the highest energy cosmic rays
The Pierre Auger Observatory has published properties of the 100 highest-energy cosmic ray events (to energies above 100 EeV) which it recorded over a 17 year period. We have examined the directional properties of these events and have taken particular note of the most energetically extreme events. We find that the most energetic events have directions which are grouped in a non-random way at the 1\% level. There is an apparent clustering in a limited region of the sky. Close to that direction …

A note on pliability and the openness of the multiexponential map in Carnot groups
Fr\'ed\'eric Jean (UMA), Mario Sigalotti (LJLL), Alessandro Socionovo (LJLL)
https://arxiv.org/abs/2507.13049

A note on pliability and the openness of the multiexponential map in Carnot groups
In recent years, several notions of non-rigidity of horizontal vectors in Carnot groups have been proposed, motivated, in particular, by the characterization of monotone sets and Whitney extension properties. In this note we compare some of these notions, proving that pliability, strong pliability, and the openness property of the multi-exponential map known as (H)-condition are all equivalent.

A note on the compactness properties of discontinuous Galerkin time discretizations
Sergio G\'omez
https://arxiv.org/abs/2509.20039 https://arxiv.org/p…

Solutions to Differential Algebraic Inequalities with Composite Bernstein Polynomials
Maxwell Hammond, Gage MacLin, Laurent Jay, Venanzio Cichella
https://arxiv.org/abs/2509.10340

Solutions to Differential Algebraic Inequalities with Composite Bernstein Polynomials
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in mind, we introduce two collocation methods for solving general ordinary differential equations using composite Bernstein polynomials to preserve the basis properties while improving convergence. Of particular note is the integration based method which uses a m…

F4 and desmic quartic surfaces
Laurent Manivel (IMT)
https://arxiv.org/abs/2508.16156 https://arxiv.org/pdf/2508.16156

F4 and desmic quartic surfaces
The desmic pencil of quartic surfaces is part of a beautiful, but mostly forgotten chapter of the classical theory of algebraic surfaces: it is the only non-degenerate pencil of surfaces in P3 containing at least three completely reducible members. We observe in this note that it is closely related to the Weyl group of the root system F4, and can be recovered from a series of symmetric spaces deduced from the exceptional Lie algebras. We discuss the main properties of the pencil from this Lie t…

On partitions associated with elementary symmetric polynomials
Cristina Ballantine, Shaheen Nazir, Bridget Eileen Tenner, Karlee Westrem, Chenchen Zhao
https://arxiv.org/abs/2510.01100

On partitions associated with elementary symmetric polynomials
The elementary symmetric partition function is a map on the set of partitions. It sends a partition lambda to the partition whose parts are the summands in the evaluation of the elementary symmetric function on the parts of lambda. These elementary symmetric partition functions have been studied before, and are related to plethysm. In this note, we study properties of the elementary symmetric partition functions, particularly related to injectivity and the number of parts appearing in their ima…

The motion of a rigid body in a viscous fluid: new results for strong solutions, uniqueness and integrability properties
Paolo Maremonti, Filippo Palma
https://arxiv.org/abs/2507.11105

The motion of a rigid body in a viscous fluid: new results for strong solutions, uniqueness and integrability properties
In this note, we show two results in the setting of Galdi-Silvestre strong solutions for the rigid body-viscous fluid interaction. The former, under an additional integrability assumption on the gradient of the initial data, proves that the time derivative of the solution belongs to $L^2(0,T;L^2(Ω))$. The latter, thanks to a further assumption only on one solution, proves that the uniqueness holds in the quoted setting. However, our extra assumption for the uniqueness is certainly verified und…

An Elementary Proof of the Nonexistence of Tarski Monster Groups of Exponent 3
Hiroshi Arai
https://arxiv.org/abs/2510.00081 https://arxiv.org/pdf/2510.000…

An Elementary Proof of the Nonexistence of Tarski Monster Groups of Exponent 3
It is well known that Tarski monster groups of exponent~3 do not exist. Traditional proofs rely on deep structural results, such as the restricted Burnside problem, properties of the free Burnside group, or Engel-type identities, and involve substantial technical computations. In this note we give a fully elementary proof: the argument reduces to a single simple identity, expressed as a key equation, whose verification requires only a brief calculation.

Note on Euler class 0 taut foliation on the Whitehead link exterior
Yao Fan, Zhentao Lai, Bin Yu
https://arxiv.org/abs/2507.14461 https://arxiv.org/pdf/250…

Note on Euler class 0 taut foliation on the Whitehead link exterior
This paper studies the existence of co-orientable taut foliations on 3-manifolds, particularly focusing on the Whitehead link exterior. We demonstrate fundamental obstructions to the existence of such foliations with certain Euler class properties, contrasting with the more permissive case of the figure-eight knot exterior. Our analysis reveals that most lattice points in the dual unit Thurston ball of the Whitehead link exterior cannot be realized as Euler classes of co-orientable taut foliati…

Elementary Proofs and Generalizations of Recent Congruences of Thejitha and Fathima
James A. Sellers
https://arxiv.org/abs/2510.01572 https://arxiv.org/pdf…

Elementary Proofs and Generalizations of Recent Congruences of Thejitha and Fathima
Motivated by recent work of Hirschhorn and the author, Thejitha and Fathima recently considered arithmetic properties satisfied by the function $a_5(n)$ which counts the number of integer partitions of weight $n$ wherein even parts come in only one color (i.e., they are monochromatic), while the odd parts may appear in one of five colors. They proved two sets of Ramanujan--like congruences satisfied by $a_5(n)$, relying heavily on modular forms. In this note, we prove their results via purely e…

On the interlacing property for zeros of Bessel functions
Dan J. Hill
https://arxiv.org/abs/2509.24612 https://arxiv.org/pdf/2509.24612

On the interlacing property for zeros of Bessel functions
This note presents a simple approach to proving the interlacing properties of positive zeros of Bessel functions of the first kind. The approach relies only on the standard recurrence relations between Bessel functions and characterising intersections between curves, providing a more accessible and intuitive understanding for the interlacing behaviour of the zeros of Bessel functions.

Augmentations, reduced ideal point gluings and compact type degenerations of curves
Valery Alexeev, Alexander Kuznetsov
https://arxiv.org/abs/2509.12429 https://

Augmentations, reduced ideal point gluings and compact type degenerations of curves
In this note we demonstrate some unexpected properties that simple gluings of the simplest derived categories may have. We consider two special cases: the first is an augmented curve, i.e., the gluing of the derived categories of a point and a curve with the gluing bimodule given by the structure sheaf of the curve; the second is an ideal point gluing of curves, i.e., the gluing of the derived categories of two curves with the gluing bimodule given by the ideal sheaf of a point in the product o…

A survey on anisotropic integral representation results
Simone Verzellesi
https://arxiv.org/abs/2509.11760 https://arxiv.org/pdf/2509.11760

A survey on anisotropic integral representation results
In this note we review some recent results concerning integral representation properties of local functionals driven by Lipschitz continuous anisotropies.

On a related note, the fibration over S¹ with fibre S¹ induced by the "flip" equivalence S¹ = S¹ should be the Klein bottle, right?
EDIT: yes

Kernelization for list $H$-coloring for graphs with small vertex cover
Marta Piecyk, Astrid Pieterse, Pawe{\l} Rz\k{a}\.zewski, Magnus Wahlstr\"om
https://arxiv.org/abs/2507.12005

Kernelization for list $H$-coloring for graphs with small vertex cover
For a fixed graph $H$, in the List $H$-Coloring problem, we are given a graph $G$ along with list $L(v) \subseteq V(H)$ for every $v \in V(G)$, and we have to determine if there exists a list homomorphism $φ$ from $(G,L)$ to $H$, i.e., an edge preserving mapping $φ: V(G)\to V(H)$ that satisfies $φ(v)\in L(v)$ for every $v\in V(G)$. Note that if $H$ is the complete graph on $q$ vertices, the problem is equivalent to List $q$-Coloring. We investigate the kernelization properties of List $H$-Co…