Finiteness theorems for matroid complexes with prescribed topology

Federico Castillo, José Alejandro Samper

Research output: Contribution to journalArticlepeer-review

Abstract

There are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating this fact 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: Are there only finitely many (d−1)-dimensional simplicial complexes with hd=k for any given k? The answer is no if we consider general complexes, but we focus on three cases coming from matroids: (i) independence complexes, (ii) broken circuit complexes, and (iii) order complexes of geometric lattices. Surprisingly, the answer is yes in all three cases.

Original languageEnglish (US)
Article number103239
JournalEuropean Journal of Combinatorics
Volume92
DOIs
StatePublished - Feb 2021
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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