The topology of the external activity complex of a matroid

Federico Ardila, Federico Castillo, Jose Alejandro Samper

Research output: Contribution to journalConference article

Abstract

We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of Las Vergnas's external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of Las Vergnas's internal order <int on M provides a shelling of the independence complex IN(M). As a corollary, Act<(M) and M have the same h-vector. We prove that, after removing its cone points, the external activity complex is contractible if M contains U3,1 as a minor, and a sphere otherwise.

Original languageEnglish (US)
Pages (from-to)73-82
Number of pages10
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2016
Externally publishedYes
Event28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada
Duration: Jul 4 2016Jul 8 2016

Keywords

  • External/internal order
  • Matroids
  • Shellability
  • Simplicial complexes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

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