The Equivariant Inverse Kazhdan--Lusztig Polynomials of Uniform Matroids

Motivated by the concepts of inverse Kazhdan--Lusztig polynomial and equivariant polynomial, Proudfoot defined for a matroid. In this paper, we show that matroid is very useful determining its polynomials, determine polynomials Boolean matroids uniform matroids. As an application, give new proof Gedeon, Proudfoot, Young's formula Inspired Lee, Nasr, Radcliffe's combinatorial interpretation ordinary matroids, further present corresponding polynomials.