2728 papers
This paper establishes an equivalence between a conjecture by Neumann and Praeger concerning Kronecker classes in algebraic number fields and a separate conjecture regarding cliques in derangement graphs within combinatorics.
This paper establishes the global rigidity of hyperbolic inversive distance circle packings on the 2-sphere, and equivalently of Koebe polyhedra in the Beltrami-Klein model, under mild assumptions on vertex links, thereby generalizing previous rigidity results and the uniqueness part of the Koebe-Andreev-Thurston Theorem to cases where adjacent circles need not touch.
This paper establishes a non-standard analysis framework that unifies coherent risk measures and their finite-sample estimators through hyperfinite representations, yielding discrete Kusuoka formulae, plug-in consistency results, and asymptotic normality via a transparent probability-to-statistics dictionary.
This paper demonstrates that the infinite random Heisenberg XXZ spin- chain exhibits slow, logarithmic information propagation characteristic of many-body localization within any arbitrary fixed energy interval, provided the interaction and disorder parameters fall within a regime determined solely by that energy interval.
This paper claims to derive a strictly closed-form, non-iterative formula for the partition function by utilizing the Simplicial Spectral Decomposition of partition polytopes within the framework of root systems and Ehrhart theory.
This paper establishes reverse square function estimates for functions with Fourier support near degenerate curves (for ), which are then applied to derive sharp Strichartz estimates for fractional Schrödinger equations on the one-dimensional torus and new local smoothing estimates in modulation spaces.
This paper establishes connections between the infinite and finite sunflower properties and canonical Ramsey properties for countable ultrahomogeneous relational structures, proving their equivalence or implication under specific conditions and demonstrating that these properties hold for various classes including free amalgamation classes and finite metric spaces.
This paper introduces a scalable semantic search system for a corpus of 9.2 million mathematical theorems, demonstrating that representing theorems with natural-language descriptions significantly improves retrieval accuracy for both specific theorems and entire papers compared to existing baselines.
This paper presents new constructions of capsets in using algebraic equations over field extensions, specifically yielding the smallest known complete capsets with sizes proportional to the best known lower bounds.
This paper establishes a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties by characterizing extendable Demazure roots, thereby providing a criterion for their reductivity and proving the K-unstability of certain -bundles over rational homogeneous spaces.
This paper demonstrates that a canonical extension of generalized Dynkin diagrams generates families of Kac-Moody groups, such as the series relevant to string theory, which satisfy homological stability and exhibit emergent structures upon stabilization, utilizing homotopy decompositions of their classifying spaces.
This paper investigates the number of isomorphism types of Banach spaces for compact spaces of a given weight, proving that there are exactly $2^\kappa\kappa\omega_12^{\omega_1}$) depends on additional set-theoretic axioms such as the Continuum Hypothesis or Baumgartner's axiom.
This paper develops a game-theoretic framework to analyze the incentives and efficiency losses in informal, privatized transit systems, demonstrating that targeted interventions like centralized routing and cross-subsidization can effectively mitigate performance gaps between decentralized profit-driven operations and optimal system outcomes.
This paper proposes a novel class of covariate-adaptive randomization procedures that effectively balance specified covariates while ensuring the asymptotic variance of unspecified covariate imbalances does not exceed that of simple randomization, thereby avoiding inflated variances and the associated "shift problem" that invalidates standard treatment effect tests.
This paper introduces a "ghost particle" method that preserves the total particle count during coalescence events, thereby enabling the derivation of exact determinant formulas for arbitrary coalescence patterns in Markovian particle systems ranging from discrete lattices to continuous diffusions.
This paper constructs a monoidal category of representations for the quantum affine algebra of a simple, simply connected, simply laced algebraic group, whose Grothendieck ring contains a cluster algebra with an initial seed corresponding to the coordinate ring of twisted products of flag varieties, including braid varieties and reduced double Bruhat cells.
This paper introduces a ghost particle method to derive exact determinantal and Pfaffian formulas for computing annihilation probabilities in particle systems, effectively overcoming the challenge of variable particle counts by treating annihilated particles as invisible walkers and extending these results to coalescence and various stochastic processes.
This paper constructs a smooth projective complex surface with a representable Chow group of 0-cycles that lacks a universal 0-cycle, thereby providing a two-dimensional analogue to Voisin's counterexample and yielding the first known instance of a smooth projective threefold of Kodaira dimension zero with a non-torsion, non-algebraic Hodge class of degree 4.
This paper demonstrates that a lightweight, automated AI pipeline integrating next-generation large language models with citation-based verification can successfully generate and solve sophisticated, research-grade mathematical problems, including previously unpublished questions, with verified results and open-sourced tools.
This paper establishes the existence and uniqueness of solutions to G-SVIEs under time-varying and integral-Lipschitz conditions using Picard iteration, while also proving the continuity of solutions with respect to parameters in the Lipschitz case.