292 papers
This paper presents three families of modular Nahm sums for symmetrizable matrices of indices and with arbitrary rank , extending previous results for low ranks and utilizing these families to construct two vector-valued automorphic forms.
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 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 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 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 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 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 resolves the isomorphism problem for reduced finitary power monoids of cancellative monoids by proving that if one monoid is torsion, the power monoids are isomorphic if and only if the base monoids are, thereby confirming the result for torsion groups while leaving the general group case open.
This paper establishes a combinatorial-cut characterization of minimal forts in trees to derive new bounds on their cardinality and count, while providing a four-part classification of trees that achieve the lower bound on the number of minimal forts.
This paper introduces a conductance-weighted fractional arboricity for graphs, establishing sharp global bounds, deriving new conductance-resistance inequalities using effective resistances, and characterizing its algebraic structure as a max-invariant within a commutative idempotent monoid under edge-disjoint unions.
This paper investigates the 2-switch-degree of a graph, defined as the degree of the graph within its realization graph, by analyzing active and inactive vertices, deriving explicit computation formulas, and examining the property's behavior in specific graph families like trees and unicyclic graphs.
This paper establishes that the natural closure operator on a graph's vertex set, defined by a set and its neighbors, induces a canonical convergence structure, which the authors analyze using nets to relate combinatorial graph properties to convergence-theoretic characteristics.
This paper establishes that for a set of phylogenetic trees with leaves, if is sufficiently small (specifically ), the trees can be constructed to have virtually no common structure, thereby forcing any network displaying them to require nearly the maximum possible number of reticulations, .
This paper employs the localization framework to improve existing upper bounds on the number of cliques in graphs with bounded maximum degree or path length, while also providing structural characterizations of the extremal graphs that attain these sharper bounds.
This paper initiates a comprehensive study of -free graph drawings by establishing tight upper and lower bounds on edge density for every combination of drawing style, graph type, and forbidden cell type, while also characterizing simple graphs that admit drawings avoiding specific cell types and improving existing bounds for quasiplanar drawings.
This paper generalizes the Atiyah problem and the Atiyah–Sutcliffe conjectures by introducing the -amplitude function, a tensor-based geometric inequality defined on finite graphs that recovers the original conjectures when the graph is complete.
This paper derives exact formulas for the proportions of derangements and derangements of -power order in various affine classical groups, utilizing a new generating function for specific integer partitions in the unitary case and verifying -polynomial identities in the symplectic and orthogonal cases.
This paper proves that every triangle-free graph with sufficiently large chromatic number contains an induced subgraph that is either a -sun for some large or a $4t$-suns in such graphs.
This paper proves that for any forest and any hereditary class of theta-free graphs excluding and the line graphs of all subdivisions of some wall, the treewidth is bounded by a polynomial function of the clique number, a result shown to be optimal as both exclusion conditions are necessary.
This paper establishes a correspondence between multiplicity-free, self-dual fusion rings and digraph-hypergraph pairs to characterize these rings via graphical properties and to classify all non-isomorphic instances of rank at most 8.