[hal-01184369] NBC Complexes of Convex Geometries

We introduce a notion of a \emphbroken circuit and an \emphNBC complex for an (abstract) convex geometry. Based on these definitions, we shall show the analogues of the Whitney-Rota's formula and Brylawski's decomposition theorem for broken circuit complexes on matroids for convex geometries. We also present an Orlik-Solomon type algebra on a convex geometry, and show the NBC generating theorem. This note is on the same line as the studies in [nakamura03a, okamoto-nakamura, nakamura].

from HAL : Dernières publications http://ift.tt/1UISe9f