Related papers: How many delta-matroids are there?
We classify all matroids with at most 8 elements that have the half-plane property, and we provide a list of some matroids on 9 elements that have, and that do not have the half-plane property. Furthermore, we prove that several classes of…
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
We show upper and lower bounds for angles in iterations of trisections of certain triangulations.
We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its…
Matroid is a generalization of many fundamental objects in combinatorial mathematics , and matroid intersection problem is a classical subject in combinatorial optimization . However , only the intersection of two matroids are well…
The twist polynomial of a delta-matroid was recently introduced by Yan and Jin, who proved a characterization of binary delta-matroids with twist monomials. In this paper, we extend this result to all delta-matroids by proving that any…
We give upper bounds on the order of the automorphism group of a simple graph
We give upper and lower bounds on the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian…
We give an upper bound on the number of perfect matchings in simple graphs with a given number of vertices and edges. We apply this result to give an upper bound on the number of 2-factors in a directed complete bipartite balanced graph on…
For each proper minor-closed subclass $\cM$ of the $\GF(q^2)$-representable matroids containing all simple $\GF(q)$-representable matroids, we give, for all large $r$, a tight upper bound on the number of points in a rank-$r$ matroid in…
We show that the basis graph of an even delta-matroid is Hamiltonian if it has more than two vertices. More strongly, we prove that for two distinct edges $e$ and $f$ sharing a common end, it has a Hamiltonian cycle using $e$ and avoiding…
Lower bounds for some explicit decision problems over the complex numbers are given.
We give some lower bounds on the Shelah rank of varieties in the free group whose coordinate groups are hyperbolic towers.
We prove an upper bound for the number of cyclic transitive subgroups in a finite permutation group and clarify the structure of the groups for which this bound becomes sharp. We also give an application in the theory of number fields.
We provide a unified framework in which the interlace polynomial and several related graph polynomials are defined more generally for multimatroids and delta-matroids. Using combinatorial properties of multimatroids rather than…
We develop a notion of {\em inner rank} as a tool for obtaining lower bounds on the rank of matrix multiplication tensors. We use it to give a short proof that the border rank (and therefore rank) of the tensor associated with $n\times n$…
Matroid theory is often thought of as a generalization of graph theory. In this paper we propose an analogous correspondence between embedded graphs and delta-matroids. We show that delta-matroids arise as the natural extension of graphic…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.
In this paper, we survey results regarding the interlace polynomial of a graph, connections to such graph polynomials as the Martin and Tutte polynomials, and generalizations to the realms of isotropic systems and delta-matroids.