The topology of the external activity complex of a matroid

Federico Ardila; Federico Castillo; Jose Alejandro Samper

The topology of the external activity complex of a matroid

Federico Ardila, Federico Castillo, Jose Alejandro Samper

Research output: Contribution to journal › Conference article › peer-review

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 language	English (US)
Pages (from-to)	73-82
Number of pages	10
Journal	Discrete Mathematics and Theoretical Computer Science
State	Published - 2016
Externally published	Yes
Event	28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada Duration: Jul 4 2016 → Jul 8 2016

Keywords

External/internal order
Matroids
Shellability
Simplicial complexes

ASJC Scopus subject areas

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

Cite this

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title = "The topology of the external activity complex of a matroid",

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 ",

keywords = "External/internal order, Matroids, Shellability, Simplicial complexes",

author = "Federico Ardila and Federico Castillo and Samper, {Jose Alejandro}",

note = "Funding Information: Partially supported by the US National Science Foundation CAREER Award DMS-0956178 and the SFSU-Colombia Combinatorics Initiative. The first author would like to thank Adam Boocher; this project would not exist without our collaboration in [1], and the numerous conversations with him on this topic. The second author would like to Isabella Novik for the invitation to the University of Washington, where part of this project was carried on. This project started at the Encuentro Colombiano de Combinatoria (ECCO 14) and we would like to thank the SFSU-Colombia Combinatorics Initiative and the Universidad de Los Andes for hosting and funding the event. Funding Information: The first author would like to thank Adam Boocher; this project would not exist without our collaboration in [1], and the numerous conversations with him on this topic. The second author would like to Isabella Novik for the invitation to the University of Washington, where part of this project was carried on. This project started at the Encuentro Colombiano de Combinatoria (ECCO 14) and we would like to thank the SFSU-Colombia Combinatorics Initiative and the Universidad de Los Andes for hosting and funding the event. Funding Information: †Email: federico@sfsu.edu. Partially supported by the US National Science Foundation CAREER Award DMS-0956178 and the SFSU-Colombia Combinatorics Initiative. Publisher Copyright: {\textcopyright} 2016 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 ; Conference date: 04-07-2016 Through 08-07-2016",

year = "2016",

language = "English (US)",

pages = "73--82",

journal = "Discrete Mathematics and Theoretical Computer Science",

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AU - Castillo, Federico

AU - Samper, Jose Alejandro

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PY - 2016

Y1 - 2016

N2 - 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

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The topology of the external activity complex of a matroid

Abstract

Keywords

ASJC Scopus subject areas

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