18 papers
Matroid analogues of Gal's conjecture
Basile Coron, Luis Ferroni, Shiyue Li
Well-known conjectures of Charney--Davis, Gal, and Nevo--Petersen predict increasingly strong positivity phenomena for the -vectors of flag simplicial spheres. In this paper, we…
There are matroid toric ideals without quadratic Gröbner bases
Jesús A. De Loera, Luis Ferroni, Santiago Morales +1
Our paper shows that if a matroid contains the Fano plane or its dual as a minor, then its toric ideal does not have any quadratic Gröbner basis. More than 25 years ago, Hibi, Her…
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 fun…
Dual Chow polynomials of matroids and posets
Giovanni Caiolo, Luis Ferroni, Elena Hoster
We introduce and study dual Chow functions associated to kernels in incidence algebras of weakly ranked posets. Given a kernel, its dual Chow function is defined as the Chow functi…
Kazhdan-Lusztig polynomials of Dowling geometries
Luis Ferroni, Matt Larson
We give a concrete combinatorial interpretation of the coefficients of the Kazhdan-Lusztig polynomials of Dowling geometries, a family of matroids which generalizes braid matroids…
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…