14 citations · 46 across the 16 of their papers we have counts for
18 papers · 1 filter
Augmented singular cohomology, uniform matroids, and real-rootedness
Kyle Binder, Lorenzo Vecchi
We study the singular cohomology rings of toric varieties associated with several fans arising from uniform matroids. These rings generalize the Chow and augmented Chow rings of ma…
A master theorem for topological zeta functions of matroids
Luis Ferroni, Lorenzo Vecchi
We study the topological zeta function of a loopless matroid and its Möbius transform. We provide a novel and manifest description (a ``Master Theorem'') for both func…
The Poincaré polynomial of the type B analogue of
Luis Ferroni, Roberto Pagaria, Lorenzo Vecchi
We establish formulas for the Poincaré polynomial of the type B analogue of the Deligne--Knudsen--Mumford moduli space of rational curves with marked points, providing type B c…
Existence of Kähler algebras with Chow polynomials as Hilbert series
Adam Schweitzer, Lorenzo Vecchi
In this article, we study Chow polynomials of weakly ranked posets and prove the existence of Gorenstein algebras with the Kähler package such that their Hilbert--Poincaré series a…
Chow classes of matroids and standard Young tableaux
Jon Pål Hamre, Benjamin Schröter, Lorenzo Vecchi +1
We study the Chow classes of arbitrary matroids in the Grassmannian. We develop a new combinatorial approach for computing them, by first focusing on snake matroids and then extend…
Extending the ab-index
Elena Hoster, Christian Stump, Lorenzo Vecchi
We prove for finite, graded, bounded posets, that the Poincaré-extended ab-index is obtained from the ab-index via the omega-transformation. This proves a conjecture by Dorpalen-Ba…
Chow polynomials of totally nonnegative matrices and posets
Petter Brändén, Lorenzo Vecchi
Huh-Stevens and Ferroni-Schröter independently conjectured that Hilbert-Poincaré series of Chow rings of geometric lattices have only real zeros. Ferroni, Matherne and the second a…
Building sets, Chow rings, and their Hilbert series
Christopher Eur, Luis Ferroni, Jacob P. Matherne +2
We establish formulas for the Hilbert series of the Chow ring of a polymatroid using arbitrary building sets. For braid matroids and minimal building sets, our results produce new…
Chow polynomials of uniform matroids are real-rooted
Petter Brändén, Lorenzo Vecchi
June Huh and Matthew Stevens conjectured that the Hilbert-Poincaré series of the Chow ring of any matroid is a polynomial with only real zeros. We prove this conjecture for the cla…
Chow functions for partially ordered sets
Luis Ferroni, Jacob P. Matherne, Lorenzo Vecchi
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 comb…
Deletion formulas for equivariant Kazhdan-Lusztig polynomials of matroids
Luis Ferroni, Jacob P. Matherne, Lorenzo Vecchi
We study equivariant Kazhdan--Lusztig (KL) and -polynomials of matroids. We formulate an equivariant generalization of a result by Braden and Vysogorets that relates the equivar…
Categorical valuative invariants of polyhedra and matroids
Ben Elias, Dane Miyata, Nicholas Proudfoot +1
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…
Inductive and divisional posets
Roberto Pagaria, Maddalena Pismataro, Tan Nhat Tran +1
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 in…
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…
Equivariant Kazhdan-Lusztig theory of paving matroids
Trevor Karn, George Nasr, Nicholas Proudfoot +1
We study the way in which equivariant Kazhdan-Lusztig polynomials, equivariant inverse Kazhdan-Lusztig polynomials, and equivariant Z-polynomials of matroids change under the opera…
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…
On matroid modularity and the coefficients of the inverse Kazhdan-Lusztig polynomial of a matroid
Lorenzo Vecchi
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…
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…