5 citations · 5 across the 8 of their papers we have counts for
10 papers
Presheaf structures governed by oriented matroids and pseudohyperplane arrangements
Basile Coron, Denis Lyskov
We study higher complements of pseudohyperplane arrangements and the specialization maps between them, induced by degenerations. We develop a presheaf formalism on oriented matroid…
Chow polynomials and chain polynomials of matroids are not log-concave
Gergely Bérczi, Basile Coron, Christopher Eur +1
The Hilbert--Poincaré series of the Chow rings of the toric varieties of matroids, often called the \emph{Chow polynomials}, and the -polynomial of their boundary complexes, cal…
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…
Structural properties of nested set complexes
Basile Coron, Luis Ferroni, Shiyue Li
We study structural and topological properties of nested set complexes of matroids with arbitrary building sets, proving that these complexes are vertex decomposable and admit conv…
Chow polynomials of rank-uniform labeled posets
Basile Coron, Luis Ferroni, Shiyue Li
We introduce and develop the theory of UMEL-shellable posets. These are posets equipped with an edge-lexicographical labeling satisfying certain uniformity and monotonicity propert…
Matroid complexes and Orlik-Solomon algebras
Basile Coron
In this article we construct a combinatorial quasi-free differential graded model for the Orlik-Solomon algebra of supersolvable matroids, which generalizes in a matroidal setting…
An algebraic interpretation of Eulerian polynomials, derangement polynomials, and beyond, via Gröbner methods
Basile Coron
Motivated by the question of whether Chow polynomials of matroids have only real roots, this article revisits the known relationship between Eulerian polynomials and the Hilbert se…
Operadic Kazhdan-Lusztig-Stanley theory
Basile Coron
We introduce a new type of operad-like structure called a P-operad, which depends on the choice of some collection of posets P, and which is governed by chains in posets of P. We i…
Supersolvability of built lattices and Koszulness of generalized Chow rings
Basile Coron
We give an explicit quadratic Grobner basis for generalized Chow rings of supersolvable built lattices, with the help of the operadic structure on geometric lattices introduced in…
Matroids, Feynman categories, and Koszul duality
Basile Coron
We show that various combinatorial invariants of matroids such as Chow rings and Orlik--Solomon algebras may be assembled into "operad-like" structures. Specifically, one obtains s…