Abstract. We study equivariant Kazhdan–Lusztig (KL) and [Formula: see text]-polynomials of matroids. We formulate an equivariant generalization of a result by Braden and Vysogorets that relates the equivariant KL and [Formula: see text]-polynomials of a matroid with those of a single-element deletion. We also discuss the failure of equivariant [Formula: see text]-positivity for the [Formula: see text]-polynomial. As an application of our main result, we obtain a formula for the equivariant KL polynomial of the graphic matroid gotten by gluing two cycles. Furthermore, we compute the equivariant KL polynomials of all matroids of corank 2 via valuations. This provides an application of the machinery of Elias et al. to corank 2 matroids, and it extends results of Ferroni and Schröter.

We introduce a class of posets, which includes both ribbon posets (skew shapes) and $d$-complete posets, such that their number of linear extensions is given by a determinant of a matrix whose entries are products of hook lengths. We also give $q$-analogues of this determinantal formula in terms of the major index and inversion statistics. As applications, we give families of tree posets whose numbers of linear extensions are given by generalizations of Euler numbers, we draw relations to Naruse and Okada's positive formulas for the number of linear extensions of skew $d$-complete posets, and we give polynomiality results analogous to those of descent polynomials by Diaz-López, Harris, Insko, Omar, and Sagan.