Work

Deletion Formulas for Equivariant Kazhdan–Lusztig Polynomials of Matroids

Year: 2025

Type: article

Abstract: . We study equivariant Kazhdan–Lusztig (KL) and [Formula: see text]-polynomials of matroids. We formulate an equivariant generalization of a result by Braden and Vysogorets that relates the equivariant KL and [Formula: see text]-polynomials of a matroid with those of a single-element deletion. We also discuss the failure of equivariant [Formula: see text]-positivity for the [Formula: see text]-polynomial. As an application of our main result, we obtain a formula for the equivariant KL polynomial of the graphic matroid gotten by gluing two cycles. Furthermore, we compute the equivariant KL polynomials of all matroids of corank 2 via valuations. This provides an application of the machinery of Elias et al. to corank 2 matroids, and it extends results of Ferroni and Schröter.

Source: SIAM Journal on Discrete Mathematics

DOI: 10.1137/24m1673796

Authors: Luis Ferroni, Jacob P. Matherne, Lorenzo Vecchi

Institutions: Institute for Advanced Study, North Carolina State University, KTH Royal Institute of Technology

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, Vetenskapsrådet

Awards: G3135660230, Alcoved polytopes - a pathway between geometry and combinatorics, G712881263