Finiteness theorems for matroid complexes with prescribed topology

Federico Castillo, José Alejandro Samper

Research output: Contribution to conferencePaperpeer-review

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 d 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.

Original languageEnglish (US)
StatePublished - 2019
Event31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia
Duration: Jul 1 2019Jul 5 2019

Conference

Conference31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019
Country/TerritorySlovenia
CityLjubljana
Period7/1/197/5/19

Keywords

  • Broken circuit complexes
  • Geometric lattices
  • Matroids

ASJC Scopus subject areas

  • Algebra and Number Theory

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