Topic: The combinatorics of matriod Kazhdan-Lusztig polynomials
Speaker: Professor Yang Libo
Event date: 5/14/2019
Event time: 15:00
Venue: Lecture Hall 1506, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract: The Kazhdan-Lusztig polynomial of a matroid was introduced by Elias, Proudfoot and Wakefield, whose properties need to be further explored. In this talk we shall give an explicit formula for computing the Kazhdan-Lusztig polynomials of arbitrary uniform matroids, which enables us to derive Gedeon, Proudfoot and Young's formula. We also prove that the Kazhdan-Lusztig polynomials of fan matroids coincide with Motzkin polynomials, which was conjectured by Gedeon.
We further obtain explicit formulas of the Kazhdan-Lusztig polynomials of wheel matroids and whirl matroids. In addition, we shall talk about the real-rootedness of these Kazhdan-Lusztig polynomials.