341 papers
This paper completes the classification of measures on Cameron's elementary treelike Fraïssé classes by establishing a bijection for -colored rooted binary trees that yields infinite families of novel semisimple tensor categories with superexponential growth, while simultaneously proving the nonexistence of such measures on -colored and labeled tree classes for .
This paper demonstrates that any non-adaptive -query relaxed locally decodable code (RLDC) with sufficiently small soundness error can be converted into a standard -query locally decodable code (LDC) with comparable parameters, thereby generalizing previous separation results and yielding improved lower bounds for RLDCs, relaxed locally correctable codes (RLCCs), and probabilistically checkable proofs of proximity (PCPPs).
This paper constructs linear codes over finite fields from arbitrary simplicial complexes by linking their topological properties to coding parameters, enabling the explicit control of code metrics through geometric operations and the creation of optimal binary codes.
This paper extends the characterization of Hoffman colorability to all connected graphs with smallest eigenvalue at least by classifying generalized line graphs and exceptional graphs, while identifying 29 maximal exceptional graphs and 39 maximal -representable graphs.
This paper establishes asymptotic formulas for the face numbers of a specific family of Hanner polytopes, a result that nearly saturates the FLM inequality for a corresponding set of parameters.
This paper resolves a question posed by Benedetti and Sagan by constructing a sign-reversing involution on Takeuchi's expansion to explicitly determine the antipode of the ring of symmetric functions in the Schur basis.
This paper presents an explicit coordinate description of the dual cosmological polytope and derives its canonical form through two distinct triangulations based on maximal and almost maximal tubings of the underlying graph, the latter of which yields a novel expression for the form.
This paper investigates the adjacency spectra of alternating-oriented -gonal staircase digraphs by demonstrating that their nonzero eigenvalues form regular -gons derived from a totally nonnegative core, establishing a three-term recursion for their characteristic polynomials, and proving that their spectral radius converges to as the staircase length increases.
This paper establishes tight sufficient conditions based on spectral radius and completely characterizes the corresponding extremal graphs for the existence of rainbow Hamilton paths and cycles in families of bipartite graphs using the bi-shifting technique.
This paper presents a concise new proof of Van der Waerden's Theorem using algebra in the compact space of ultrafilters , distinguishing itself from existing proofs by avoiding the use of minimal or idempotent ultrafilters.
This paper extends the characterization of signed graphs with exactly two main eigenvalues from the case where the associated multigraph has a tree base to the case where the base graph is unicyclic, concluding with several proposed open problems.
This paper investigates and compares the properties of q-Narayana polynomials specifically at the values and .
This paper improves the known lower bound on the size of transitive subgraphs in -majority tournaments from to , demonstrating an exponential improvement in the dependence of the exponent on .
This paper initiates a systematic study of arrow pattern avoidance in permutations by establishing structural results such as arrow-Wilf equivalence and enumerating various avoidance classes, including those involving pairs of patterns that prohibit fixed points.
This paper investigates paths in the p-Bratteli diagram for odd primes to prove the vanishing of sign balance from inversions and to define new families of -Fibonacci numbers based on descents, which generalize the OEIS sequence A391520.
This paper presents a randomized polynomial-time algorithm for learning read-once determinants by establishing its equivalence to a black-box version of the Principal Minor Assignment Problem and resolving the latter through the introduction of the rank-one extension property.
This paper investigates the plane geometry of -rationals by constructing deformed Farey triangulations and modular surfaces, interpreting these numbers as Ford-like circles, and introducing Springborn operations as quadratic generalizations of Farey addition that correspond geometrically to the homothety centers of circle pairs.
This paper demonstrates that for Kautz graphs with sufficiently large diameters, a regular routing scheme achieves a better all-to-all makespan than any shortest-path routing scheme by proving the existence of edges with congestion strictly exceeding the regular routing's step count.
This paper generalizes Backhausz and Szegedy's result on the infinite regular tree by proving that the Gaussian wave is the unique typical process with Green's function covariance for any infinite tree of finite cone type satisfying mild expansion, thereby establishing the convergence of local eigenvector distributions to the Gaussian wave for random bipartite biregular graphs and generic configuration models.
This paper introduces the concept of abelian-normal numbers by adapting abelian complexity functions to digit expansions, constructs a non-normal analogue of Champernowne's constant that satisfies this new property, and proposes open problems regarding its behavior.