Journal ArticleThe Combinatorics Behind the Leading Kazhdan-Lusztig Coefficients of Braid MatroidsGao, Alice LL; Proudfoot, Nicholas James; Yang, Arthur LB; Zhang, Zhong-Xue<p>Ferroni and Larson gave a combinatorial interpretation of the braid Kazhdan-Lusztig polynomials in terms of series-parallel matroids. As a consequence, they confirmed an explicit formula for the leading Kazhdan-Lusztig coefficients of braid matroids with odd rank, as conjectured by Elias, Proudfoot, and Wakefield. Based on Ferroni and Larson’s work, we further explore the combinatorics behind the leading Kazhdan-Lusztig coefficients of braid matroids. The main results of this paper include an explicit formula for the leading Kazhdan-Lusztig coefficients of braid matroids with even rank, a simple expression for the number of simple series-parallel matroids of rank $k + 1$ on $2k$ elements, and explicit formulas for the leading coefficients of inverse Kazhdan-Lusztig polynomials of braid matroids. The binomial identity for the Abel polynomials plays an important role in the proofs of these formulas.</p>Electronic Journal of Combinatorics2024-07-1210580758The Electronic Journal of Combinatorics3131077-8926https://doi.org/10.37236/127782344861; 2053243National Science Foundation