Kazhdan-Lusztig Polynomials of Thagomizer Matroids

Katie R. Gedeon

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.

Keywords


Matroid theory; Kazhdan-Lusztig polynomials; Generating functions; Schur functions

Full Text:

PDF