The inverse Kazhdan-Lusztig polynomial of a matroid

In analogy with the classical Kazhdan-Lusztig polynomials for Coxeter groups, Elias, Proudfoot and Wakefield introduced concept of matroids. It is known that both matroid can be considered as special cases Kazhdan-Lusztig-Stanley locally finite posets. framework polynomials, we study inverse functions define We also compute these boolean matroids uniform As an unexpected application obtain a new formula to Similar polynomial matroid, conjecture coefficients its are nonnegative log-concave.