Mathematics, Department of

 

Department of Mathematics: Dissertations, Theses, and Student Research

First Advisor

Kyungyong Lee

Second Advisor

Jamie Radcliffe

Date of this Version

8-2021

Document Type

Dissertation

Citation

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 Radcliffe

Lincoln, Nebraska, August 2021

Comments

Copyright © 2021, George David Nasr. Used by permission

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.

Advisors: Kyungyong Lee and Jamie Radcliffe

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