318 papers
This paper introduces an overpartition analogue of Andrews and Dastidar's partition function , deriving its generating function and establishing congruences modulo 3, 5, and powers of 2 using classical -series identities.
This paper presents an optimized "optimize-then-refine" framework combining mixed-integer nonlinear programming with exact symbolic computation to solve Heilbronn's triangle problem for with certified global optimality in minutes, thereby proving the optimality of a 2002 configuration and deriving exact coordinates for through $9$.
This paper extends the concept of super-minimally -connected matroids to the case of , determining the maximum size of such rank- matroids and characterizing those that achieve this extremal bound, thereby paralleling previous results for minimally $23$-connected matroids.
This paper determines explicit formulas for the special values of the spectral zeta function on regular trees at positive integers, reveals unexpected symmetries between values at positive and negative integers, and establishes a functional equation of the type for a natural completion of the function.
This paper investigates conditions under which sumsets involving difference sets or almost Bohr sets contain Bohr sets, demonstrating that specific sparse sets like squares and shifted primes satisfy these properties and applying these results to generalize findings on central sets and recurrence in discrete abelian groups.
This paper proves a weaker version of a conjecture by Chudnovsky et al. regarding tree decompositions for graphs excluding and the grid as induced minors, demonstrating that such graphs admit decompositions where bag independence numbers are bounded by polylogarithmic functions under specific distance constraints.
This paper provides a complete characterization of graphs satisfying the equation , thereby solving an open problem posed by Levit and Mandrescu and extending known results from graphs with a unique odd cycle to a broader family containing arbitrarily many odd cycles.
This paper provides a complete structural classification of 2-bicritical odd-bicyclic graphs into four families using ear-pendant decompositions, explicitly computing their maximum independent sets, cores, and coronas to establish precise relationships between these parameters and the relative positions of the graphs' odd cycles.
This paper establishes that for graphs with at most two odd cycles, the sum of the sizes of the core and corona is tightly bounded by the independence number, provides precise characterizations for these values and the core-corona partition, and demonstrates that computing the core, corona, and independence number for this class is solvable in polynomial time.
This paper demonstrates that certain directed graphs with identical vertex sets but distinct arc sets yield the same sum of arborescence weights for a given root, establishing a connection to the Matrix-Tree Theorem and offering a graphical method for factoring matrix determinants.
This paper investigates the structure and large genus asymptotics of certain Hurwitz numbers by utilizing the value of the central character on transpositions.
This paper generalizes the large genus asymptotics of Hurwitz numbers from the Riemann sphere to arbitrary compact Riemann surfaces, specifically for cases involving a fixed number of general profiles and some profiles.
Using tropical geometry, the authors prove that the genus of the configuration curves for planar linkages derived from minimally rigid graphs is generically odd, except in cases where it is zero.
This paper establishes an explicit combinatorial interpretation for the -polynomial of the arbor polytopes , proves their Ehrhart polynomials are magic positive and their -polynomials are real-rooted via a new parking model, and conjectures a general combinatorial interpretation for all arbor polytopes.
This paper improves a known theorem on the existence of 2-connected subgraphs of all intermediate orders in graphs with minimum degree at least , while disproving two conjectures by Yin and Wu regarding conditions based on edge count and minimum degree, and proposing a new conjecture for sufficiently large graphs.
This paper generalizes the role of the abstract chromatic number in determining the asymptotics of Turán-type functions to other graph parameters, providing proofs and two specific examples of this extension.
This paper proves that there are only finitely many prime critically 4-frustrated and 5-frustrated signed graphs, thereby confirming the Steffen-Naserasr conjecture for the cases and .
This paper improves the known upper bounds on the maximum number of tangencies among 1-intersecting Jordan arcs from to for the general case and to for the strictly 1-intersecting case, while also establishing tighter bounds for specific variants involving -monotone curves and proving a new graph-theoretic result.
This paper introduces a new graph game called "Agents and Adversary," a variation of Cops and Robbers, by classifying infinite graph families as winning for either side, defining a new symmetry to establish an Adversary winning strategy, and providing tight bounds on the Agents' time-to-win.
This paper demonstrates that the second-order term in the scaling limit of the identity element for the abelian sandpile group on finite Sierpinski gasket graphs converges to the path distance to the nearest corner, a result established by decomposing the identity into a constant function and the Laplacian of the graph distance.