Algebraic shifting of cyclic polytopes and stacked polytopes

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Gil Kalai introduced the shifting-theoretic upper bound relation as a method to generalize the g-theorem for simplicial spheres by using algebraic shifting. We will study the connection between the shifting-theoretic upper bound relation and combinatorial shifting. Also, we will compute the exterior algebraic shifted complex of the boundary complex of the cyclic d-polytope as well as of a stacked d-polytope. It will turn out that, in both cases, the exterior algebraic shifted complex coincides with the symmetric algebraic shifted complex.

Original languageEnglish
Pages (from-to)1707-1721
Number of pages15
JournalDiscrete Mathematics
Volume307
Issue number14
DOIs
Publication statusPublished - 2007 Jun 28
Externally publishedYes

Fingerprint

Polytopes
Polytope
Upper bound
Generalise
Theorem

Keywords

  • Algebraic shifting
  • Simplicial polytopes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Algebraic shifting of cyclic polytopes and stacked polytopes. / Murai, Satoshi.

In: Discrete Mathematics, Vol. 307, No. 14, 28.06.2007, p. 1707-1721.

Research output: Contribution to journalArticle

@article{7b4c710de1f9410ba42a8f5449ea4e2a,
title = "Algebraic shifting of cyclic polytopes and stacked polytopes",
abstract = "Gil Kalai introduced the shifting-theoretic upper bound relation as a method to generalize the g-theorem for simplicial spheres by using algebraic shifting. We will study the connection between the shifting-theoretic upper bound relation and combinatorial shifting. Also, we will compute the exterior algebraic shifted complex of the boundary complex of the cyclic d-polytope as well as of a stacked d-polytope. It will turn out that, in both cases, the exterior algebraic shifted complex coincides with the symmetric algebraic shifted complex.",
keywords = "Algebraic shifting, Simplicial polytopes",
author = "Satoshi Murai",
year = "2007",
month = "6",
day = "28",
doi = "10.1016/j.disc.2006.09.018",
language = "English",
volume = "307",
pages = "1707--1721",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "14",

}

TY - JOUR

T1 - Algebraic shifting of cyclic polytopes and stacked polytopes

AU - Murai, Satoshi

PY - 2007/6/28

Y1 - 2007/6/28

N2 - Gil Kalai introduced the shifting-theoretic upper bound relation as a method to generalize the g-theorem for simplicial spheres by using algebraic shifting. We will study the connection between the shifting-theoretic upper bound relation and combinatorial shifting. Also, we will compute the exterior algebraic shifted complex of the boundary complex of the cyclic d-polytope as well as of a stacked d-polytope. It will turn out that, in both cases, the exterior algebraic shifted complex coincides with the symmetric algebraic shifted complex.

AB - Gil Kalai introduced the shifting-theoretic upper bound relation as a method to generalize the g-theorem for simplicial spheres by using algebraic shifting. We will study the connection between the shifting-theoretic upper bound relation and combinatorial shifting. Also, we will compute the exterior algebraic shifted complex of the boundary complex of the cyclic d-polytope as well as of a stacked d-polytope. It will turn out that, in both cases, the exterior algebraic shifted complex coincides with the symmetric algebraic shifted complex.

KW - Algebraic shifting

KW - Simplicial polytopes

UR - http://www.scopus.com/inward/record.url?scp=34147164423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34147164423&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2006.09.018

DO - 10.1016/j.disc.2006.09.018

M3 - Article

VL - 307

SP - 1707

EP - 1721

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 14

ER -