299 papers
This paper introduces combinatorics on words through the lens of low factor complexity in infinite words, exploring their minimal complexity, formalizing non-triviality, and presenting new algebraic proofs and consequences for classical theorems by Morse, Hedlund, and Tijdeman.
This paper presents a highly symmetric 6-dimensional polytope whose antipodal quotient yields a 24-vertex triangulation of , conjectured to be minimal, while also providing improved 45- and 49-vertex triangulations for .
This paper introduces the concept of orthogonal decomposability for convex polytopes using orthogonal connectedness, analyzing its application to Platonic and Archimedean solids while identifying examples of polytopes that do not possess this property.
This paper constructs and proves the existence of an infinite sequence of strongly regular digraphs with parameters by utilizing block circulant matrices, polynomial arithmetic, and computational tools to derive explicit adjacency formulas and propose a conjecture regarding their automorphism groups.
This paper resolves a problem posed by Bang-Jensen and Wang by proving that every 6-strong split digraph is 2-linked, and further establishes that every 5-strong semicomplete split digraph is 2-linked, a bound shown to be tight.
This paper proves a conjecture by Dong et al. regarding the negativity of the -th derivative of the logarithm of the chromatic polynomial with a negative variable for all and , where is the graph's maximum degree.
This paper establishes spectral upper bounds for the independence number of graphs and even uniform hypergraphs, extends the Hoffman bound to these structures, and provides a simple spectral condition to determine key graph parameters including the independence number, Shannon capacity, and Lovász number.
This paper demonstrates that any two forests or pseudoforests sharing the same degree sequence can be transformed into one another via a sequence of 2-switches while preserving their forest or pseudoforest structure, and further establishes that this operation minimally perturbs specific integer parameters, thereby proving these parameters possess the interval property within these graph families.
This survey reviews the computation of Weil-Petersson and Masur-Veech volumes for moduli spaces of Riemann surfaces, highlighting their profound impact on combinatorial enumeration, intersection theory, and recursion relations, while drawing parallels between the methods used to calculate these two distinct types of volumes.
This paper establishes a combinatorial sufficient condition based on multinet structures for the Milnor fiber of a complex hyperplane arrangement to be non-1-formal and uses this criterion to construct an infinite family of monomial arrangements with non-formal Milnor fibers.
This paper establishes four equivalent combinatorial conditions proving that the maximum number of Hamiltonian sets of polygonal paths in a simple assembly graph of size is , a bound achieved exclusively by graphs known as tangled cords.
This paper proposes sum rules for the moments of permutations with a fixed number of fixed points involving Stirling numbers of the first kind, while also deriving related identities for binomial coefficients and outlining connections to Bell numbers.
This paper establishes a comparison between the Segre motivic Chern classes of open projected Richardson varieties and affine Schubert cells via the affine Grassmannian using Demazure–Lusztig operators, while also relating these classes to twisted Kazhdan–Lusztig R-polynomials and providing a combinatorial formula for the Grassmannian case.
This paper presents an elementary, self-contained proof of the Lovász Local Lemma that eliminates the need for conditional probabilities by relying solely on unconditional probability inequalities.
This paper establishes conditions for the distance integrality of specific graph families constructed via joins with cycles and for the distance Laplacian integrality of a particular class of dumbbell graphs.
This paper establishes a base change framework to extend tensor function results from specific fields to general fields, thereby proving that slice rank is linearly bounded by geometric rank and is quasi-supermultiplicative for any 3-tensors over any field.
This paper addresses an Erdős-Herzog-Piranian problem by proving that the maximum product of distances for diameter-2 point sets can be found among convex polygons, providing improved constructions over regular -gons and demonstrating that a general characterization of extremal polygons is impossible for even orders.
This paper introduces the class of -cuttable undirected phylogenetic networks as a computationally useful alternative to tree-child-orientable networks, demonstrating that they are recognizable in polynomial time and render the NP-hard Tree Containment problem solvable in polynomial time for .
This paper derives explicit formulas for general position polynomials of complete multipartite graphs and investigates their unimodality and log-concavity, demonstrating that these properties hold for balanced complete multipartite graphs with small part sizes and for coronas of various graph classes, while failing for larger part sizes.
The paper proves the existence of a partial -system whose Ramsey number with colors exhibits tower-type growth of height .