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
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
Comments
Copyright © 2021, George David Nasr. Used by permission