Algebraic shifting and strongly edge decomposable complexes

Research output: Contribution to conferencePaper

Abstract

Let Γ be a simplicial complex with n vertices, and let Δ(Γ) be either its exterior algebraic shifted complex or its symmetric algebraic shifted complex. If Γ is a simplicial sphere, then it is known that (a) Δ(Γ) is pure and (b) h-vector of Γ is symmetric. Kalai and Sarkaria conjectured that if Γ is a simplicial sphere then its algebraic shifting also satisfies (c) Δ (Γ) ⊂ Δ (C(n; d)), where C(n; d) is the boundary complex of the cyclic d-polytope with n vertices. We show this conjecture for strongly edge decomposable spheres introduced by Nevo. We also show that any shifted simplicial complex satisfying (a), (b) and (c) is the algebraic shifted complex of some simplicial sphere.

Original languageEnglish
Pages1-12
Number of pages12
Publication statusPublished - 2008 Dec 1
Externally publishedYes
Event20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile
Duration: 2008 Jun 232008 Jun 27

Other

Other20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
CountryChile
CityValparaiso
Period08/6/2308/6/27

Keywords

  • Algebraic shifting
  • Simplicial spheres
  • Squeezed spheres
  • The strong Lefschetz property

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Murai, S. (2008). Algebraic shifting and strongly edge decomposable complexes. 1-12. Paper presented at 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08, Valparaiso, Chile.