The topology of the external activity complex of a matroid

Federico Ardila, Federico Castillo, Jose Alejandro Samper Casas

Research output: Contribution to journalArticle

Abstract

We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of LasVergnas’s external/internal order <ext=int on M provides a shelling of Act<(M). We also show that every linear extension of LasVergnas’s internal order <int on M provides a shelling of the in- dependence 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 U1;3 as a minor, and a sphere otherwise.

Original languageEnglish (US)
JournalElectronic Journal of Combinatorics
Volume23
Issue number3
StatePublished - Jan 1 2016
Externally publishedYes

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Matroid
Cones
Linear Extension
Topology
H-vector
Internal
Minor
Corollary
Cone

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this

The topology of the external activity complex of a matroid. / Ardila, Federico; Castillo, Federico; Samper Casas, Jose Alejandro.

In: Electronic Journal of Combinatorics, Vol. 23, No. 3, 01.01.2016.

Research output: Contribution to journalArticle

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