Related papers: K-classes of delta-matroids and equivariant locali…
We introduce two families of symmetric functions with an extra parameter t that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when t = 1. The families are defined by a statistic on…
In this paper, we focus on the equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids, a natural family of graphic matroids associated with the complete tripartite graphs $K_{1,1,n}$. These polynomials were introduced by…
Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroid. We prove his conjecture that a positroid is exactly an intersection of…
We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a \emph{stressed subset}. This framework provides a new combinatorial characterization of the class of split…
We characterize the cone of GL-equivariant Betti tables of Cohen-Macaulay modules of codimension 1, up to rational multiple, over the coordinate ring of square matrices. This result serves as the base case for `Boij-S\"oderberg theory for…
In contrast to matroids, vf-safe delta-matroids have three kinds of minors and are closed under the operations of twist and loop complementation. We show that the delta-matroids representable over GF(4) with respect to the nontrivial…
In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…
We construct a combinatorial generalization of the Leray models for hyperplane arrangement complements. Given a matroid and some combinatorial blowup data, we give a presentation for a bigraded (commutative) differential-graded algebra. If…
The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n x n skew-symmetric matrix. Its points correspond to n-dimensional isotropic subspaces of a 2n-dimensional vector space. In this paper we…
We considered the possibility that the oriented matroid theory is connected with supersymmetry via the Grassmann-Plucker relations. The main reason for this, is that such relations arise in both in the chirotopes definition of an oriented…
Isomorphy classes of k-involutions have been studied for their correspondence with generalized symmetric spaces of algebraic groups. This is a continuation of papers written by A.G. Helminck and collaborators that are regarding algebraic…
We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality…
We introduce and study the notion of the $G$-Tutte polynomial for a list $\mathcal{A}$ of elements in a finitely generated abelian group $\Gamma$ and an abelian group $G$, which is defined by counting the number of homomorphisms from…
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering…
We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and $1432$-avoiding permutations via tableau combinatorics. These formulas generalize a formula for degrees of symmetric Grothendieck polynomials which…
One of the most important classes of even $\Delta$-matroids arises from orientable ribbon graphs, which play a role analogous to that of graphic matroids in matroid theory. Motivated by a natural correspondence between strong…
In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters…
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a…
The equivariant Kazhdan-Lusztig polynomial of a braid matroid may be interpreted as the intersection cohomology of a certain partial compactification of the configuration space of n distinct labeled points in the plane, regarded as a graded…
A positroid is a matroid realized by a matrix such that all maximal minors are non-negative. Positroid polytopes are matroid polytopes of positroids. In particular, they are lattice polytopes. The Ehrhart polynomial of a lattice polytope…