English

Kazhdan-Lusztig polynomials of matroids under deletion

Combinatorics 2023-06-13 v3

Abstract

We present a formula which relates the Kazhdan-Lusztig polynomial of a matroid MM, as defined by Elias, Proudfoot and Wakefield, to the Kazhdan--Lusztig polynomials of the matroid obtained by deleting an element, and various contractions and localizations of MM. We give a number of applications of our formula to Kazhdan--Lusztig polynomials of graphic matroids, including a simple formula for the Kazhdan--Lusztig polynomial of a parallel connection graph.

Keywords

Cite

@article{arxiv.1909.09888,
  title  = {Kazhdan-Lusztig polynomials of matroids under deletion},
  author = {Tom Braden and Artem Vysogorets},
  journal= {arXiv preprint arXiv:1909.09888},
  year   = {2023}
}

Comments

21 pages, two figures. Fixed small error in introduction