Kazhdan-Lusztig polynomials of matroids under deletion (Q2290343)

Summary: We present a formula which relates the Kazhdan-Lusztig polynomial of a matroid \(M\), as defined by \textit{B. Elias} et al. [Adv. Math. 299, 36--70 (2016; Zbl 1341.05250)], to the Kazhdan-Lusztig polynomials of the matroid obtained by deleting an element, and various contractions and localizations of \(M\). We give a number of applications of our formula to Kazhdan-Lusztig polynomials of graphic matroids, including a simple formula for the Kazhdan-Lusztig polynomial of a parallel connection graph.