# Probability/Combinatorics Seminar

This seminar is held on Thursdays at 2pm in 210 Deady Hall.

### Winter Quarter, 2017

- January 26,
**Katie Gedeon** (UO)

Kazhdan-Lusztig polynomials of thagomizer graphs
**Abstract**: To a graph G, one can associate a polynomial with non-negative integer coefficients called the Kazhdan-Lusztig polynomial of G. More generally, you can obtain the Kazhdan-Lusztig polynomial of any matroid, but today we will focus on the specialization to graphs. The Kazhdan-Lusztig theory for matroids was developed in analogy with the classical theory for Coxeter groups, though there are some important differences which I will touch on lightly. In this talk, we will construct the defining recursion for the Kazhdan-Lusztig polynomial of thagomizer graphs and use this obtain a closed form for the coefficients of the polynomial. No prior knowledge of matroids or Kazhdan-Lusztig polynomials will be assumed.