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arXiv:2606.00633v1 Announce Type: new Abstract: The $P(t)$-adic Littlewood conjecture is a function field analogue of the famous $p$-adic Littlewood conjecture in Diophantine approximation. In this paper, we prove that the $P(t)$-adic Littlewood conjecture fails for any irreducible polynomial $P(t)$ over any ground field of odd characteristic.
arXiv:2606.00638v1 Announce Type: new Abstract: We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \geq H^*:=\sup_{0
arXiv:2606.00639v1 Announce Type: new Abstract: We apply ideas of geometric measure theory and Baire category theory to topological problems, namely, to topological embeddings of compact sets into Euclidean spaces. In 1947, Borsuk constructed a Cantor set in $\mathbb R^N$, $N\geqslant 3$, such that its projection onto any $(N-1)$-plane contains an $(N-1)$-dimensional ball. This can be strengthened: a desired Cantor set can be obtained fro....
arXiv:2606.00646v1 Announce Type: new Abstract: Motivated by a recent conjecture of Bsila, Cox, Hugo, Styron and Zhuang concerning fixed points and pixed points on pattern-avoiding permutations, we prove a bivariate refinement involving descent statistics. Given a set of permutations $\Pi$, let $\mathfrak{S}_n(\Pi)$ denote the set of permutations in the symmetric group $\mathfrak{S}_n$ that avoid every element of $\Pi$ in the sense of patt..
arXiv:2606.00648v1 Announce Type: new Abstract: We study multiple point ranges for random walks on graphs, extending known asymptotic results obtained for random walks on groups. A distinctive feature is that algebraic and translation-invariance assumptions are replaced by a uniform tail condition on the first return time to the starting point. Under this condition, we obtain upper and lower bounds of linear order for the expectations of t..
arXiv:2606.00650v1 Announce Type: new Abstract: We develop a deterministic framework showing that a power-law form of semi-uniform localization of eigenfunctions (SULE) imposes strong structural and dynamical constraints on lattice operators. In particular, we prove that power-law SULE yields geometric constraints on localization centers, quantitative bounds on eigenfunction correlators, and power-law localization in the sense of finite mo....
arXiv:2606.00653v1 Announce Type: new Abstract: Let $G$ be a simple connected graph, and let $T_{G}(x,y)$ be the Tutte polynomial of $G$. Motivated by the works in \cite{Ma}, we, in this paper, introduce the even-left spanning forests of $G$ and odd $G$-partitionable permutations, and show that $T_{G}(2,-1)$ is equal to both the number of even-left spanning forests of $G$ and the number of odd $G$-partitionable permutations. In particular,..
arXiv:2606.00659v1 Announce Type: new Abstract: A gradient flow for the concentration and a $2\times 2$ tensor is constructed to describe smectic liquid crystals. The free energy consists of the entropy term and interaction term involving squared second order spatial derivatives. The entropy term incorporates the concentration in the quasi-entropy originally proposed for the tensor only, which is a strictly convex and lower semicontinuous ....
arXiv:2606.00668v1 Announce Type: new Abstract: Semantic communications which can significantly reduce spectrum consumption in wireless networks, have recently become a popular research area. When combined with wireless power transfer (WPT), semantic communications can help achieve high spectral efficiency for energy-limited devices in wireless communications. In energy-constrained and link budget-limited scenarios such as UAV networks, th....
AHA! RSK - arxiv.org - 1 month ago - eng
arXiv:2606.00679v1 Announce Type: new Abstract: We give a spectral realization of the Robinson-Schensted-Knuth (RSK) correspondence in terms of the representation theory of the symmetric group $S_n$ and the degenerate affine Hecke algebra (AHA) $H_n$. We view RSK, which builds a pair of standard Young tableaux from a permutation, as a special case of rectification, also known as Jeu de Taquin, which turns skew tableaux into straight ones. ....
arXiv:2606.00687v1 Announce Type: new Abstract: From a generating function for a Legendrian in a $1$-jet bundle, we may extract the following topological information: (1) a trivialization of the stable Gauss map, (2) the sheaf of sub-level-set stable cohomotopies, and (3) an identification of the microlocalization of the latter with the J-homomorphism image of the former. Here we show that in fact (1), (2), (3) completely classify generati..
arXiv:2606.00691v1 Announce Type: new Abstract: We solve, for all sufficiently large even orders, the problem proposed by Chen et al. on sharp $A_\alpha$-spectral conditions for the existence of odd $[1,b]$-factors when $\alpha>1/2$. Chen et al. showed that every connected graph of even order $n$ with no odd $[1,b]$-factor has $A_\alpha$-spectral radius at most $\max_{1\le s\le k}\rho_\alpha(G_s)$, where $G_s=K_s\nabla\left(K_{n-(b+1)s-1}\....
arXiv:2606.00693v1 Announce Type: new Abstract: We define a bi-invariant word metric on a group using keis. We discuss whether such a word metric is trivial or non-trivial in various examples coming from group theory, dynamical systems, as well as complex and symplectic geometry.
arXiv:2606.00703v1 Announce Type: new Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible. We study a B-bit quantized stochastic first-order oracle: an optimizer interacts for T rounds and receives, each round, a B-bi....
arXiv:2606.00707v1 Announce Type: new Abstract: Motivated by the small-scale viewpoint of Roff and Yoshinaga, we study finite metric spaces whose scaled copies collapse to a single point while their magnitude remembers how the collapse takes place. The limit metric space is geometrically indistinguishable from a point, but the magnitude function can detect differences in the path of collapse. We introduce a four-parameter family of cyclic ..
arXiv:2606.00710v1 Announce Type: new Abstract: High-dimensional environmental systems often contain variables that are strongly predictive, structurally informative, and physically coupled, but these roles are not equivalent. In precipitation dynamics, this distinction is particularly important because rainfall emerges from multiscale thermodynamic, kinematic, microphysical, and land--atmosphere interactions, while observations are sparse....
arXiv:2606.00713v1 Announce Type: new Abstract: This paper is concerned with the Liouville-type problem for the stationary fractional compressible magnetohydrodynamics (MHD) equations. The main difficulty comes from the nonlocal fractional Laplace operator $(-\Delta)^s$. To overcome it, we combine the Caffarelli-Silvestre extension technique with truncation arguments. Under suitable regularity and decay conditions, we prove that the only s..
arXiv:2606.00719v1 Announce Type: new Abstract: Let $\kappa^{\prime}(G)$ be the edge-connectivity of the graph $G$. The \textit{strength} of $G$, denoted by $\overline{\kappa}^{\prime}(G)$, is the maximum edge-connectivity of its subgraphs. A simple graph $G$ is called $k$-\textit{edge-maximal} if $\overline{\kappa}^{\prime}(G) \leq k$ but for any edge $e$ not in $G$, $\overline{\kappa}^{\prime}(G+e) \geq k+1$. In this paper, we propose th..
arXiv:2606.00731v1 Announce Type: new Abstract: In this paper, we introduce and study the notion of Q-filters in bounded lattices.
arXiv:2606.00736v1 Announce Type: new Abstract: We prove that, over any ring $R$, the supremum of the projective dimensions of the flat left $R$-modules coincides with the supremum of the Gorenstein projective dimensions of the Gorenstein flat left $R$-modules. As a consequence, we obtain new characterizations of left $n$-perfect rings in terms of Gorenstein projective, Ding projective, and projectively coresolved Gorenstein flat dimension..
arXiv:2606.00760v1 Announce Type: new Abstract: We introduce Schur-Agler class for the pentablock $\mathbb P$ and establish a realization theorem for functions in this class. Then we prove an interpolation theorem for the pentablock with interpolating functions belonging to the corresponding Schur-Agler class. Also, we obtain an extension theorem for $\mathbb P$. Applying these results, we add a few new characterizations in the existing re..
arXiv:2606.00764v1 Announce Type: new Abstract: We show that the Gaussian Gabor system at the critical density is a weighted lower semi frame, thus resolving an open question. This complements recent results showing that the system is neither a weighted frame nor admits a reproducing partner. In fact, after removing any atom from the system, suitable weights produce a complete Riesz Fischer sequence and lower semi frame.
arXiv:2606.00772v1 Announce Type: new Abstract: Let $\lambda = (\lambda_1, \ldots, \lambda_n)$ be a partition with $\lambda_1 = m$. Denote by $J_\lambda$ the cover ideal in the polynomial ring \( S = k[x_1, \ldots, x_n, y_1, \ldots, y_m] \) associated to the Ferrers graph corresponding to $\lambda$. Let $d(\lambda)$ denote the number of distinct parts of $\lambda$. We prove that \[ \operatorname{pd}(S/J_\lambda^t) = \min\{t,\; d(\lambda)\}..
arXiv:2606.00778v1 Announce Type: new Abstract: Variational inequality (VI) is a fundamental mathematical framework for many classical problems. We present a path-following framework for finite-dimensional VIs with arbitrary continuous functions and compact convex domains. The approach first approximately reduces a general VI to a smooth VI on simplex. Its key innovation is to formulate the smooth VI on simplex on a fiber bundle called the....
arXiv:2606.00781v1 Announce Type: new Abstract: We introduce a continuous-time mutation model with two types determined by a finite measure $\Lambda$ on the unit interval. The model satisfies a certain consistency property known from mathematical population genetics and includes so called harmonic models being of interest in mathematical statistical physics. We mainly focus on the situation when the number of particles is equal to some con..
arXiv:2606.00792v1 Announce Type: new Abstract: Electrifying truck fleets has the potential to improve energy efficiency and reduce carbon emissions from the freight transportation sector. However, the range limitations and substantial capital costs with current battery technologies imposes constraints that challenge the overall cost feasibility of electrifying fleets for logistics companies. In this paper, we investigate the coupled routi....
arXiv:2606.00799v1 Announce Type: new Abstract: A classic theorem of Weyl (1921) states that a Weyl metric -- a natural generalisation of a pseudo-Riemannian metric -- is uniquely determined by its conformal and projective structures (i.e. by its conformal structure and its set of unparametrised geodesics). An equivalent formulation of Weyl's result is that a torsion-free linear connection compatible with a pseudo-Riemannian conformal stru..
arXiv:2606.00802v1 Announce Type: new Abstract: Given a graph $G$, a set $F$ of edges is an edge dominating set of $G$ if every edge in $G$ is either in $F$ or adjacent to an edge in $F$. A graph $G$ is said to be well-edge-dominated if every minimal edge dominating set has the same cardinality. This definition is the edge version of domination in that a set $D\subseteq V(G)$ is a dominating set if every vertex in $G$ is in $D$ or adjacent..
arXiv:2606.00812v1 Announce Type: new Abstract: We define a new Ehrenfeucht-Fra\"iss\'e game for dependence logic. The previously known rendition of such a game was based on moves that are teams. Since teams can be massive, making team moves may be quite complicated. To remedy this, our new Ehrenfeucht-Fra\"iss\'e game for dependence logic has only moves that consist of single elements, as in the classical Ehrenfeucht-Fra\"iss\'e game of f..
arXiv:2606.00833v1 Announce Type: new Abstract: We prove the Nielsen--Schreier property for the variety of algebras defined by the identity $x(x^2)^2=(x^2)^2x$: every subalgebra of every free algebra in this variety is itself free. We also show that this variety of algebras does not have the Poincar\'e--Birkhoff--Witt property for universal multiplicative enveloping algebras. Our strategy of proof actually leads to infinitely many new vari..
arXiv:2606.00836v1 Announce Type: new Abstract: Graphs defined over finite rings are well studied in the literature. The study of these graphs benefits from rich connections between several areas of mathematics, including number theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over..
arXiv:2606.00843v1 Announce Type: new Abstract: Let $G$ be a simple graph with degree diagonal matrix $D(G)$ and adjacency matrix $A(G)$. The signless Laplacian matrix of $G$ is defined as $Q(G)=D(G)+A(G)$. For a real number $\alpha \in [0, 1]$, Nikiforov (2017) proposed the $A_\alpha$-matrix of a graph $G$ as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$. The $A_\alpha$-spectral radius of $G$, denoted by $\rho_\alpha(G)$, is the largest eige....
arXiv:2606.00845v1 Announce Type: new Abstract: In this article we study the notion of completeness for conjunctive reducibilities. We investigate the relationship between $c$-completeness and $r$-completeness of computably enumerable (c.e.) sets with respect to various strong reducibilities $\le_r$. By using simplicity properties of sets, we prove that there exist c.e. sets that are simultaneously $Q$-complete and $bd$-complete, yet fail ..
arXiv:2606.00850v1 Announce Type: new Abstract: We state and prove a Toeplitz corona theorem for the pentablock $\mathbb{P}$, a domain in $\mathbb{C}^3$ given by \[ \mathbb{P}=\{(a_{21}, \text{tr}(A), \det(A)) \in \mathbb C^3 : A=[a_{ij}] \in M_2(\mathbb C), \|A\|<1\}. \] By two different applications of this theorem, we obtain a few new characterizations in the Toeplitz corona theorems for the bidisc and the symmetrized bidisc.
arXiv:2606.00853v1 Announce Type: new Abstract: We present and analyze Frank-Wolfe with Moreau Envelope Smoothing (FRAMES) for solving nonsmooth nonconvex constrained optimization problems, taking advantage of iterative smoothing via the Moreau envelope followed by one Frank-Wolfe step per iteration. The problem template we consider encompasses splitting problems with multiple convex constraint sets as well as problems with nonsmooth weakl....
arXiv:2606.00855v1 Announce Type: new Abstract: We propose constrained neural parameterization schemes for several classes of constraints arising in optimization problems in function spaces. This is achieved by constructing smooth neural parameterizations whose image lies entirely in the admissible set while remaining asymptotically dense. In this way, the original constrained optimization problem is transformed into a smooth unconstrained..
arXiv:2606.00861v1 Announce Type: new Abstract: Powell introduced the Axiom of Double Complement ($\mathsf{DCom}$) to give his double-negation interpretation of $\mathsf{ZF}$ into $\mathsf{IZF_{Rep}}$. However, the consistency, strength, and compatibility of $\mathsf{DCom}$ remain open problems. This article aims to survey the compatibility and consistency strength of $\mathsf{DCom}$, its consequence and opposites, which will be named $\ma..
arXiv:2606.00863v1 Announce Type: new Abstract: We study the generation problem in the Higman-Thompson groups $F_n$ via the core and closure of subgroups of $F_n$ and associated automata. We give sufficient conditions for a subset $X \subseteq F_n$ to generate $F_n$, and provide an algorithm which verifies these conditions when $X$ is finite. As an application, we answer a question of Aiello and Nagnibeda, motivated by Savchuk's problem on..
arXiv:2606.00865v1 Announce Type: new Abstract: It is shown that any hyponormal operator on an infinite-dimensional separable Hilbert space that admits a decomposition \( T = R + V \), where \( R \) is tridiagonal and \( V \) is trace-class, has nontrivial closed hyperinvariant subspaces provided $T$ is not a multiple of the identity. We further discuss implications of this result for the invariant subspace problem of hyponormal operators ..
arXiv:2606.00868v1 Announce Type: new Abstract: We study the distribution of indecomposable elements in Euclidean lattices. A positive element in a lattice is called indecomposable if it cannot be represented as a sum of two other positive nonzero elements. The set of all indecomposables in a lattice forms the Hilbert basis for the positive lattice semigroup. We classify lattices that contain only finitely many indecomposables versus those..
arXiv:2606.00870v1 Announce Type: new Abstract: We consider natural Hamiltonian systems with potentials that are $C^0$ or $C^1$ on a hypersurface and $C^{\infty}$-smooth in the complement and introduce and study corresponding notions of their integrabilty and non-integrability. As a motivating example, we derive and analyze models of bungee jumping. We provide prototype examples of the Liuoville-Arnol'd theorem for $C^0$ and $C^1$ Hamilton..
arXiv:2606.00876v1 Announce Type: new Abstract: In this article, we study the space of smooth genus one curves on del Pezzo threefolds of degree 4 and 5. We describe the irreducible components of the Kontsevich moduli space generically parametrizing genus one stable maps with irreducible domains and classify the irreducible components of the morphism space from general elliptic curves. Our result verifies the Geometric Manin's conjecture f..
arXiv:2606.00879v1 Announce Type: new Abstract: Corresponding to weak almost contact metric structures (defined recently by Rovenski and Wolak), we introduce and study here weak almost contact structures with B-metric, which generalize the classical almost contact structures with Norden metric (B-metric). Several geometric properties are obtained, some special classes are investigated and a lot of examples are constructed throughout this w..
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