The Γ-vector of a barycentric subdivision

Eran Nevo; T. Kyle Petersen; Bridget Eileen Tenner

doi:10.1016/j.jcta.2011.01.001

The Γ-vector of a barycentric subdivision

Eran Nevo^*, T. Kyle Petersen, Bridget Eileen Tenner

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We prove that the γ-vector of the barycentric subdivision of a simplicial sphere is the f-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the h-vector of the barycentric subdivision of a boolean complex.

Original language	English
Pages (from-to)	1364-1380
Number of pages	17
Journal	Journal of Combinatorial Theory. Series A
Volume	118
Issue number	4
DOIs	https://doi.org/10.1016/j.jcta.2011.01.001
State	Published - May 2011
Externally published	Yes

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (E. Nevo), [email protected] (T.K. Petersen), [email protected] (B.E. Tenner). 1 The author was partially supported by an NSF Award DMS-0757828.

Keywords

Charney-Davis conjecture
F-vector
Gal's conjecture
γ-vector

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10.1016/j.jcta.2011.01.001

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title = "The Γ-vector of a barycentric subdivision",

abstract = "We prove that the γ-vector of the barycentric subdivision of a simplicial sphere is the f-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the h-vector of the barycentric subdivision of a boolean complex.",

keywords = "Charney-Davis conjecture, F-vector, Gal's conjecture, γ-vector",

author = "Eran Nevo and Petersen, {T. Kyle} and Tenner, {Bridget Eileen}",

note = "Funding Information: E-mail addresses: [email protected] (E. Nevo), [email protected] (T.K. Petersen), [email protected] (B.E. Tenner). 1 The author was partially supported by an NSF Award DMS-0757828.",

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AU - Tenner, Bridget Eileen

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N2 - We prove that the γ-vector of the barycentric subdivision of a simplicial sphere is the f-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the h-vector of the barycentric subdivision of a boolean complex.

AB - We prove that the γ-vector of the barycentric subdivision of a simplicial sphere is the f-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the h-vector of the barycentric subdivision of a boolean complex.

KW - Charney-Davis conjecture

KW - F-vector

KW - Gal's conjecture

KW - γ-vector

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JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 4

ER -

The Γ-vector of a barycentric subdivision

Abstract

Bibliographical note

Keywords

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