22 citations · 134 across the 13 of their papers we have counts for
13 papers
Examples and counterexamples in Ehrhart theory
Luis Ferroni, Akihiro Higashitani
This article provides a comprehensive exposition about inequalities that the coefficients of Ehrhart polynomials and -polynomials satisfy under various assumptions. We pay par…
Kazhdan-Lusztig polynomials of braid matroids
Luis Ferroni, Matt Larson
We provide a combinatorial interpretation of the Kazhdan--Lusztig polynomial of the matroid arising from the braid arrangement of type , which gives an interpreta…
Hilbert-Poincaré series of matroid Chow rings and intersection cohomology
Luis Ferroni, Jacob P. Matherne, Matthew Stevens +1
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, t…
Valuative invariants for large classes of matroids
Luis Ferroni, Benjamin Schröter
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…
The Merino--Welsh conjecture for split matroids
Luis Ferroni, Benjamin Schröter
In 1999 Merino and Welsh conjectured that evaluations of the Tutte polynomial of a graph satisfy an inequality. In this short article we show that the conjecture generalized to mat…
Lattice points in slices of prisms
Luis Ferroni, Daniel McGinnis
We conduct a systematic study of the Ehrhart theory of certain slices of rectangular prisms. Our polytopes are generalizations of the hypersimplex and are contained in the larger c…
Stressed hyperplanes and Kazhdan-Lusztig gamma-positivity for matroids
Luis Ferroni, George D. Nasr, Lorenzo Vecchi
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 pe…
Ehrhart polynomials of rank two matroids
Luis Ferroni, Katharina Jochemko, Benjamin Schröter
Over a decade ago De Loera, Haws and Köppe conjectured that Ehrhart polynomials of matroid polytopes have only positive coefficients and that the coefficients of the corresponding…
Matroids are not Ehrhart positive
Luis Ferroni
In this article we disprove the conjectures asserting the positivity of the coefficients of the Ehrhart polynomial of matroid polytopes by De Loera, Haws and Köppe (2007) and of ge…
Matroid relaxations and Kazhdan-Lusztig non-degeneracy
Luis Ferroni, Lorenzo Vecchi
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 depe…
Integer point enumeration on independence polytopes and half-open hypersimplices
Luis Ferroni
In this paper we investigate the Ehrhart Theory of the independence matroid polytope of uniform matroids. It is proved that these polytopes have an Ehrhart polynomial with positive…
On the Ehrhart Polynomial of Minimal Matroids
Luis Ferroni
We provide a formula for the Ehrhart polynomial of the connected matroid of size and rank with the least number of bases, also known as a minimal matroid. We prove that the…
Hypersimplices are Ehrhart Positive
Luis Ferroni
We consider the Ehrhart polynomial of hypersimplices. It is proved that these polynomials have positive coefficients and we give a combinatorial formula for each of them. This sett…