Séminaire Lotharingien de Combinatoire, 82B.99 (2019), 12 pp.

Federico Castillo and José Alejandro Samper

Finiteness theorems for matroid complexes with prescribed topology

Abstract. It is known that there are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating to the language of h-vectors, there are finitely many simplicial complexes of bounded dimension with h1=k for any natural number k. In this paper we study the question at the other end of the h-vector: given d and k there are only finitely many -1-dimensional independence complexes, broken circuit complexes, and order complexes of geometric lattices (without coloops) with hd=k. This suggests new upper/lower bound programs for these types of simplicial complexes.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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