Flawlessness of $h$-vectors of broken circuit complexes

Abstract

One of the major open questions in matroid theory asks whether the $h$-vector $(h_0,h_1,\dots ,h_s)$ of the broken circuit complex of a matroid $M$ satisfies the following inequalities: $$ h_0\leq h_1\leq \cdots\leq h_{\lfloor s/2\rfloor} \quad \text{and}\qua h_i\le h_{s-i}\ \text{ for }\ 0\leq i \leq \lfloor s/2\rfloor. $$ This paper affirmatively answers the question for matroids that are representable over a field of characteristic zero.

Revised version; added Remark 4.3 on the current status of Conjectures 1.1 and 4.1; to appear in Int. Math. Res. Not

References in corpus (1)

• Broken circuit complexes and hyperplane arrangements