The Kazhdan-Lusztig polynomials of uniform matroids

The Kazhdan-Lusztig polynomial of a matroid was introduced by Elias et al. (2016) [4]. Let Um,d denote the uniform rank d on set m+d elements. Gedeon (2017) [7] pointed out that they can derive an explicit formula polynomials using equivariant polynomials. In this paper we give alternative formula, which allows us to prove real-rootedness for 2?m?15 and all d's. case m=1 previously proved [8]. We further determine Z-polynomials Um,d's Our also enables proof Gedeon, Proudfoot, Young's without