7 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…
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…
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…
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…