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

24 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	American 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: nevoe@math.bgu.ac.il (E. Nevo), tkpeters@math.depaul.edu (T.K. Petersen), bridget@math.depaul.edu (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

Cite this

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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: nevoe@math.bgu.ac.il (E. Nevo), tkpeters@math.depaul.edu (T.K. Petersen), bridget@math.depaul.edu (B.E. Tenner). 1 The author was partially supported by an NSF Award DMS-0757828.",

year = "2011",

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doi = "10.1016/j.jcta.2011.01.001",

language = "American English",

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pages = "1364--1380",

journal = "Journal of Combinatorial Theory - Series A",

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T1 - The Γ-vector of a barycentric subdivision

AU - Nevo, Eran

AU - Petersen, T. Kyle

AU - Tenner, Bridget Eileen

N1 - Funding Information: E-mail addresses: nevoe@math.bgu.ac.il (E. Nevo), tkpeters@math.depaul.edu (T.K. Petersen), bridget@math.depaul.edu (B.E. Tenner). 1 The author was partially supported by an NSF Award DMS-0757828.

PY - 2011/5

Y1 - 2011/5

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

UR - http://www.scopus.com/inward/record.url?scp=78651395936&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2011.01.001

DO - 10.1016/j.jcta.2011.01.001

M3 - Article

AN - SCOPUS:78651395936

SN - 0097-3165

VL - 118

SP - 1364

EP - 1380

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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