an:06772884
Zbl 1369.05029
Gedeon, Katie R.
Kazhdan-Lusztig polynomials of thagomizer matroids
EN
Electron. J. Comb. 24, No. 3, Research Paper P3.12, 10 p. (2017).
00368384
2017
j
05B35 05A15 20C30 52B40
matroid theory; Kazhdan-Lusztig polynomials; generating functions; Schur functions
Summary: 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.