Kazhdan-Lusztig Polynomials Under Deletion

Tom Braden, Artem Vysogorets
2020 Electronic Journal of Combinatorics  
We present a formula which relates the Kazhdan–Lusztig polynomial of a matroid $M$, as defined by Elias, Proudfoot and Wakefield, 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.
doi:10.37236/9026 fatcat:mbrpr2h24ba3rp6eyp4jxuipgq