Kazhdan-Lusztig Polynomials of Thagomizer Matroids

  • Katie R. Gedeon
Keywords: Matroid theory, Kazhdan-Lusztig polynomials, Generating functions, Schur functions

Abstract

We introduce thagomizer matroids and compute the Kazhdan-Lusztig polynomial of a rank $n+1$ thagomizer matroid by showing that the coefficient of $t^k$ is equal to the number of Dyck paths of semilength $n$ with $k$ long ascents. We also give a conjecture for the $S_n$-equivariant Kazhdan-Lusztig polynomial of a thagomizer matroid.
Published
2017-07-28
Article Number
P3.12