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Colección SciELO Chile

Finiteness theorems for matroid complexes with prescribed topology

Indexado

WoS	WOS:000589912900012
Scopus	SCOPUS_ID:85091557508

DOI

10.1016/J.EJC.2020.103239

Año

2021

Tipo

artículo de investigación

Citas Totales

Autores Afiliación Chile

Instituciones Chile

% Participación
Internacional

Autores
Afiliación Extranjera

Instituciones
Extranjeras

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 h(1) = 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 h(d) = 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. (C) 2020 Elsevier Ltd. All rights reserved.

Revista

Revista	ISSN
European Journal Of Combinatorics	0195-6698

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Disciplinas de Investigación

WOS
Mathematics

Scopus
Sin Disciplinas

SciELO
Sin Disciplinas

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Publicaciones WoS (Ediciones: ISSHP, ISTP, AHCI, SSCI, SCI), Scopus, SciELO Chile.

Colaboración Institucional

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Autores - Afiliación

Ord.	Autor	Género	Institución - País
1	Castillo, Federico	Hombre	Max Planck Inst Math Sci - Alemania Max Planck Institute for Mathematics in the Sciences - Alemania
2	Samper, Jose Alejandro	Hombre	Pontificia Universidad Católica de Chile - Chile
2	Samper, José Alejandro	Hombre	Pontificia Universidad Católica de Chile - Chile

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Financiamiento

Fuente
University of Washington
University of Kansas
Max-Planck Institute for Mathematics in the Sciences

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Agradecimientos

Agradecimiento
We would like to thank Richard Stanley for interesting conversations and for pointing out the reference in his book to Theorem 5.3. Thanks to Ed Swartz for reminding us of Example 2.13. An anonymous referee pointed out the connections between geometric lattices and cosimple matroids that inspired Corollary 5.5. We are specially indebted to Isabella Novik for various interesting conversations and helpful suggestions on preliminary versions. We are grateful to the University of Washington and University of Kansas where parts of this project were carried out. The second named author also thanks the University of Miami where he was employed when most of the project was carried out. This project was completed while both authors were members of the Max-Planck Institute for Mathematics in the Sciences.

Agradecimiento

We would like to thank Richard Stanley for interesting conversations and for pointing out the reference in his book to Theorem 5.3. Thanks to Ed Swartz for reminding us of Example 2.13. An anonymous referee pointed out the connections between geometric lattices and cosimple matroids that inspired Corollary 5.5. We are specially indebted to Isabella Novik for various interesting conversations and helpful suggestions on preliminary versions. We are grateful to the University of Washington and University of Kansas where parts of this project were carried out. The second named author also thanks the University of Miami where he was employed when most of the project was carried out. This project was completed while both authors were members of the Max-Planck Institute for Mathematics in the Sciences.