6 papers · 1 filter
An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits
Raul Cordovil, David Forge
A family C of circuits of a matroid M is a linear class if, given a modular pair of circuits in C}, any circuit contained in the union of the pair is also in C. The pair (M,C) can…
Kalai orientations on matroid polytopes
Raul Cordovil
Let P a polytope and let G(P) be the graph of P. Following Gil Kalai, we say that an acyclic orientation O of G(P) is good if, for every non-empty face F of P, the induced graph G(…
A note on mixed graphs and matroids
J. Orestes Cerdeira, Raul Cordovil
A mixed graph is a graph with some directed edges and some undirected edges. We introduce the notion of mixed matroids as a generalization of mixed graphs. A mixed matroid can be v…
How is a Chordal Graph like a Supersolvable Binary Matroid?
Raul Cordovil, David Forge, Sulamita Klein
Let G be a finite simple graph. From the pioneering work of R. P. Stanley it is known that the cycle matroid of G is supersolvable iff G is chordal (rigid): this is another way to…
Diagonal bases in Orlik-Solomon type algebras
Raul Cordovil, David Forge
To encode an important property of the "no broken circuit bases" of the Orlik-Solomon-Terao algebras, Andras Szenes has introduced a particular type of bases, the so called "diagon…
Quadratic Orlik-Solomon algebras of graphic matroids
Raul Cordovil, David Forge
In this note we introduce a sufficient condition for the Orlik-Solomon algebra associated to a matroid M to be l-adic and we prove that this condition is necessary when M is binary…