On the cd-index and γ-vector of S*-shellable CW-spheres

Satoshi Murai; Eran Nevo

doi:10.1007/s00209-011-0917-4

On the cd-index and γ-vector of S*-shellable CW-spheres

Satoshi Murai, Eran Nevo^*

^*Corresponding author for this work

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

5 Scopus citations

Abstract

We show that the γ-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable CW-spheres which includes all polytopes. The proof shows that certain parts of the cd-index, when specializing c = 1 and considering the resulted polynomial in d, are the f-polynomials of simplicial complexes that can be colored with "few" colors. We conjecture that the cd-index of a regular CW-sphere is itself the flag f-vector of a colored simplicial complex in a certain sense.

Original language	English
Pages (from-to)	1309-1319
Number of pages	11
Journal	Mathematische Zeitschrift
Volume	271
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-011-0917-4
State	Published - Aug 2012
Externally published	Yes

Bibliographical note

Funding Information:
Research of the first author was partially supported by KAKENHI 22740018. Research of the second author was partially supported by an NSF Award DMS-0757828 and Marie Curie grant IRG-270923.

Keywords

Balanced simplicial complex
Polytope
cd-index
γ-vector

Access to Document

10.1007/s00209-011-0917-4

Cite this

@article{3471ad338e1b41808623a17c466a5546,

title = "On the cd-index and γ-vector of S*-shellable CW-spheres",

abstract = "We show that the γ-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable CW-spheres which includes all polytopes. The proof shows that certain parts of the cd-index, when specializing c = 1 and considering the resulted polynomial in d, are the f-polynomials of simplicial complexes that can be colored with {"}few{"} colors. We conjecture that the cd-index of a regular CW-sphere is itself the flag f-vector of a colored simplicial complex in a certain sense.",

keywords = "Balanced simplicial complex, Polytope, cd-index, γ-vector",

author = "Satoshi Murai and Eran Nevo",

note = "Funding Information: Research of the first author was partially supported by KAKENHI 22740018. Research of the second author was partially supported by an NSF Award DMS-0757828 and Marie Curie grant IRG-270923.",

year = "2012",

month = aug,

doi = "10.1007/s00209-011-0917-4",

language = "אנגלית",

volume = "271",

pages = "1309--1319",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - On the cd-index and γ-vector of S*-shellable CW-spheres

AU - Murai, Satoshi

AU - Nevo, Eran

N1 - Funding Information: Research of the first author was partially supported by KAKENHI 22740018. Research of the second author was partially supported by an NSF Award DMS-0757828 and Marie Curie grant IRG-270923.

PY - 2012/8

Y1 - 2012/8

N2 - We show that the γ-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable CW-spheres which includes all polytopes. The proof shows that certain parts of the cd-index, when specializing c = 1 and considering the resulted polynomial in d, are the f-polynomials of simplicial complexes that can be colored with "few" colors. We conjecture that the cd-index of a regular CW-sphere is itself the flag f-vector of a colored simplicial complex in a certain sense.

AB - We show that the γ-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable CW-spheres which includes all polytopes. The proof shows that certain parts of the cd-index, when specializing c = 1 and considering the resulted polynomial in d, are the f-polynomials of simplicial complexes that can be colored with "few" colors. We conjecture that the cd-index of a regular CW-sphere is itself the flag f-vector of a colored simplicial complex in a certain sense.

KW - Balanced simplicial complex

KW - Polytope

KW - cd-index

KW - γ-vector

UR - http://www.scopus.com/inward/record.url?scp=84864390825&partnerID=8YFLogxK

U2 - 10.1007/s00209-011-0917-4

DO - 10.1007/s00209-011-0917-4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84864390825

SN - 0025-5874

VL - 271

SP - 1309

EP - 1319

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

On the cd-index and γ-vector of S*-shellable CW-spheres

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this