On the NBC-complexes and β-invariants of abstract convex geometries

We present new expressions for the characteristic polynomials (chromatic polynomials) and Tutte polynomials of matroids, graphs and hyperplane arrangements. Those expressions extend Whitney's celebrated Broken Circuit Theorem, Whitney's Theorem, ...

A convex geometry is a combinatorial abstract model introduced by Edelman and Jamison which captures a combinatorial essence of ''convexity'' shared by some objects including finite point sets, partially ordered sets, trees, rooted graphs. In this paper,...

We present a number of lower bounds for the h-vectors of k-Cohen--Macaulay (k-CM), broken circuit, and independence complexes. These lead to bounds on the coefficients of the characteristic and reliability polynomials of matroids. The main techniques ...