Geodesic
Matroid relaxations and Kazhdan–Lusztig non-degeneracy
Ferroni, Luis1 ; Vecchi, Lorenzo2
1 KTH Royal Institute of Technology Department of Mathematics Stockholm Sweden
2 Università di Bologna Dipartimento di Matematica Bologna Italy
Algebraic Combinatorics, Tome 5 (2022) no. 4, pp. 745-769 Cet article a éte moissonné depuis la source Numdam

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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.

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DOI : 10.5802/alco.244
Classification : 05B35, 05E10, 52B40, 11B83
Keywords: Kazhdan–Lusztig polynomials of matroids, Circuit-hyperplane relaxations, Geometric lattices, Real-rooted polynomials

Ferroni, Luis 1 ; Vecchi, Lorenzo 2

1 KTH Royal Institute of Technology Department of Mathematics Stockholm Sweden
2 Università di Bologna Dipartimento di Matematica Bologna Italy
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Matroid relaxations and {Kazhdan{\textendash}Lusztig} non-degeneracy},
     journal = {Algebraic Combinatorics},
     pages = {745--769},
     year = {2022},
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Ferroni, Luis; Vecchi, Lorenzo. Matroid relaxations and Kazhdan–Lusztig non-degeneracy. Algebraic Combinatorics, Tome 5 (2022) no. 4, pp. 745-769. doi: 10.5802/alco.244

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