298 papers
This paper presents the first weakly polynomial-time algorithms for the parametric submodular line search problem by exploiting a dual formulation and cutting-plane methods to reduce the number of calls to the exact submodular function minimization oracle.
This paper establishes a framework for constructing Monge-Ampère measures and solving associated variational equations on balanced polyhedral spaces by leveraging convex function theory and tropical intersection, while also connecting these results to non-archimedean pluripotential theory.
This paper presents the first and lowest-order examples of 3-regular 3-edge-colored graphs that violate large factorization in Gaussian random tensor models, contrasting with the well-established factorization behavior observed in random matrices.
This paper provides a complete characterization of interval nest digraphs by introducing "nest orderings," a specific type of vertex linear ordering defined by forbidden patterns, thereby completing the set of vertex-ordering characterizations for major subclasses of interval digraphs.
This paper establishes a bijection between a generalization of tropical oriented matroids and subdivisions of root polytopes, which are sub-polytopes of a product of two simplices.
Motivated by pseudo-Gorenstein rings, this paper introduces the concept of pseudo-Gorenstein graphs and classifies them within several natural graph families using independence polynomials.
This paper confirms that G.A. Dirac's conjecture regarding the existence of pairwise order-compatible, edge-disjoint paths holds for infinite graphs with bounded path lengths and establishes that such paths form an equivalence relation for all infinite cardinals , with the full conjecture being true if and only if has uncountable cofinality.
This paper establishes that the -deformed modular group specializes to a finite group at a complex parameter if and only if is a primitive -th root of unity for , in which cases the resulting groups are isomorphic to specific binary polyhedral groups, while the case yields an infinite but "mild" structure with applications to Jones polynomials.
This paper generalizes the 2025 triplication method for constructing strong starters in by expanding the definition of triplication tables and broadening the associated Sudoku-type problem formulation, thereby eliminating the previous restriction that must not be divisible by 3 and enabling the construction of strong starters for any odd order $3m$.
This paper derives explicit formulas for the dual Drazin inverse of dual complex anti-triangular block matrices and applies these results to solve open problems and extend existing group inverse findings for the adjacency matrices of DN-DS, DN-DLS, and DN-DW digraphs.
This paper presents a polynomial-time algorithm for approximately sampling uniformly random equitable colorings when the number of colors exceeds $2\Delta$, utilizing the geometry of polynomials framework to establish a multivariate local Central Limit Theorem for color class sizes.
This paper proves that as approaches infinity, the proportion of orientably-regular maps and hypermaps with automorphism groups or that are chiral tends to 1, establishing that chirality is generic for these structures.
This paper determines the minimum sizes of -completely hyperseparating set systems for general and of $2$-hyperseparating set systems, thereby generalizing recent results by Bat'iková, Kepka, and Němec.
This paper proves that, under a mild moment condition, the number of occurrences of a fixed rooted plane tree as a general subtree in a conditioned Galton--Watson tree is asymptotically normal with linear mean and variance, thereby confirming a conjecture by Janson and demonstrating that the result fails if the moment condition is violated.
This paper introduces and systematically analyzes a variant of the Cops and Robbers game where a cop follows a predetermined patrol against an omniscient robber, determining the minimum capture radius required for various graph classes including trees, grids, and chordal graphs.
This paper generalizes Zhou's 2021 recursion for a specific constant term identity—originally conjectured by Kadell and later proved by Károlyi, Lascoux, and Warnaar—by categorizing the variables into two parts to extend the result to a broader context.
This paper introduces a matrix-based notion of matroid representation over local commutative rings using modular independence, establishing conditions under which this system forms a matroid, deriving structural properties for codes over chain rings, and demonstrating that certain non-field-representable matroids, such as the Vámos matroid, can be represented over rings like .
This paper establishes that for sufficiently large and , the maximum size of a 3-wise -intersecting family of -element subsets is , with the bound being asymptotically tight under the condition for .
This paper establishes that the graded Ehrhart theory of unimodular zonotopes yields a -evaluation of their Tutte polynomials and characterizes their harmonic algebras as finitely generated, Cohen--Macaulay coordinate rings of arrangement Schubert varieties, thereby confirming specific conjectures by Reiner and Rhoades.
This paper classifies the generating functions of genus zero lattice walks in the first quadrant with interacting boundaries by adapting a -difference equation method to show that, unlike the non-interacting case, these functions are typically hypertranscendental unless specific algebraic relations between the Boltzmann weights render them -algebraic or -rational.