A Combinatorial Formula for Kazhdan-Lusztig Polynomials of Sparse Paving Matroids

Authors

George Nasr, University of Nebraska-LincolnFollow

First Advisor

Jamie Radcliffe

Second Advisor

Kyungyong Lee

Date of this Version

8-2021

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professors Kyungyong Lee and Jamie Radclie. Lincoln, Nebraska: August, 2021

Copyright © 2021 George David Nasr

Abstract

We present a combinatorial formula using skew Young tableaux for the coefficients of Kazhdan-Lusztig polynomials for sparse paving matroids. These matroids are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. We also show the positivity of these coefficients using our formula. In special cases, such as for uniform matroids, our formula has a nice combinatorial interpretation.

Advisers: Kyungyong Lee and Jamie Radclie