Zobrazeno 1 - 10
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pro vyhledávání: '"Vecchi, Lorenzo"'
Three decades ago, Stanley and Brenti initiated the study of the Kazhdan--Lusztig--Stanley (KLS) functions, putting on common ground several polynomials appearing in algebraic combinatorics, discrete geometry, and representation theory. In the presen
Externí odkaz:
http://arxiv.org/abs/2411.04070
We study equivariant Kazhdan--Lusztig (KL) and $Z$-polynomials of matroids. We formulate an equivariant generalization of a result by Braden and Vysogorets that relates the equivariant KL and $Z$-polynomials of a matroid with those of a single-elemen
Externí odkaz:
http://arxiv.org/abs/2406.19962
We introduce the notion of a categorical valuative invariant of polyhedra or matroids, in which alternating sums of numerical invariants are replaced by split exact sequences in an additive category. We provide categorical lifts of a number of valuat
Externí odkaz:
http://arxiv.org/abs/2401.06869
Publikováno v:
J. London Math. Soc., 109 (2024)
We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their superclass
Externí odkaz:
http://arxiv.org/abs/2304.08145
Publikováno v:
Advances in Mathematics, Volume 449, July 2024, no. 109733
We study the Hilbert series of four objects arising in the Chow-theoretic and Kazhdan-Lusztig framework of matroids. These are, respectively, the Hilbert series of the Chow ring, the augmented Chow ring, the intersection cohomology module, and its st
Externí odkaz:
http://arxiv.org/abs/2212.03190
We study the way in which equivariant Kazhdan-Lusztig polynomials, equivariant inverse Kazhdan-Lusztig polynomials, and equivariant Z-polynomials of matroids change under the operation of relaxation of a collection of stressed hyperplanes. This allow
Externí odkaz:
http://arxiv.org/abs/2202.06938
Publikováno v:
Int. Math. Res. Not. IMRN 2022 rnac270
In this article we make several contributions of independent interest. First, we introduce the notion of stressed hyperplane of a matroid, essentially a type of cyclic flat that permits to transition from a given matroid into another with more bases.
Externí odkaz:
http://arxiv.org/abs/2110.08869
Publikováno v:
In Advances in Mathematics July 2024 449
Autor:
Ferroni, Luis, Vecchi, Lorenzo
Publikováno v:
Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 745-769
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
Externí odkaz:
http://arxiv.org/abs/2104.14531
Autor:
Vecchi, Lorenzo
Following the work of Gao and Xie in [2], we state some properties of the inverse Kazhdan-Lusztig polynomial of a matroid. We also give partial answers to a conjecture that states that regular connected matroids are non-degenerate. We link the degene
Externí odkaz:
http://arxiv.org/abs/2103.08580