Matroid relaxations and Kazhdan-Lusztig non-degeneracy
| Autor: | Ferroni, Luis, Vecchi, Lorenzo |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 745-769 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.5802/alco.244 |
| Popis: | In this paper we study the interplay between the operation of circuit-hyperplane relaxation and the Kazhdan--Lusztig theory of matroids. We obtain a family of polynomials, not depending on the matroids but only on their ranks, that relate the Kazhdan--Lusztig, the inverse Kazhdan--Lusztig and the $Z$-polynomial of each matroid with those of its relaxations. As an application of our main theorem, we prove that all matroids having a free basis are non-degenerate. Additionally, we obtain bounds and explicit formulas for all the coefficients of the Kazhdan--Lusztig, inverse Kazhdan--Lusztig and $Z$-polynomial of all sparse paving matroids. Comment: 25 pages. To appear in Algebraic Combinatorics |
| Databáze: | arXiv |
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