Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Ferroni, Luis"'
This article concerns the face enumeration of augmented Bergman complexes of matroids, introduced by Braden, Huh, Matherne, Proudfoot and Wang. We prove that the augmented Bergman complex of any matroid admits a convex ear decomposition and deduce th
Externí odkaz:
http://arxiv.org/abs/2410.08812
Wagner (1992) proved that the Hadamard product of two P\'olya frequency sequences that are interpolated by polynomials is again a P\'olya frequency sequence. We study the preservation under Hadamard products of related properties of significance in c
Externí odkaz:
http://arxiv.org/abs/2408.12386
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
Autor:
Ferroni, Luis, Schröter, Benjamin
We provide a full classification of all families of matroids that are closed under duality and minors, and for which the Tutte polynomial is a universal valuative invariant. There are four inclusion-wise maximal families, two of which are the class o
Externí odkaz:
http://arxiv.org/abs/2403.17696
Autor:
Ferroni, Luis
Publikováno v:
Combinatorial Theory, Vol. 3, Issue 3, 2023
We provide a combinatorial way of computing Speyer's $g$-polynomial on arbitrary Schubert matroids via the enumeration of certain Delannoy paths. We define a new statistic of a basis in a matroid, and express the $g$-polynomial of a Schubert matroid
Externí odkaz:
http://arxiv.org/abs/2311.01397
Autor:
Ferroni, Luis, Schröter, Benjamin
This paper initiates the explicit study of face numbers of matroid polytopes and their computation. We prove that, for the large class of split matroid polytopes, their face numbers depend solely on the number of cyclic flats of each rank and size, t
Externí odkaz:
http://arxiv.org/abs/2310.05487
Autor:
Ferroni, Luis, Higashitani, Akihiro
This article provides a comprehensive exposition about inequalities that the coefficients of Ehrhart polynomials and $h^*$-polynomials satisfy under various assumptions. We pay particular attention to the properties of Ehrhart positivity as well as u
Externí odkaz:
http://arxiv.org/abs/2307.10852
Autor:
Ferroni, Luis, Larson, Matt
Publikováno v:
Comm. Amer. Math. Soc. 4 (2024), 64-79
We provide a combinatorial interpretation of the Kazhdan--Lusztig polynomial of the matroid arising from the braid arrangement of type $\mathrm{A}_{n-1}$, which gives an interpretation of the intersection cohomology Betti numbers of the reciprocal pl
Externí odkaz:
http://arxiv.org/abs/2303.02253
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
Autor:
Ferroni, Luis, Schröter, Benjamin
Publikováno v:
Journal of the London Mathematical Society, Vol. 110(3), Sep. 2024, e12984
We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a \emph{stressed subset}. This framework provides a new combinatorial characterization of the class of split matroids. Mor
Externí odkaz:
http://arxiv.org/abs/2208.04893