Algebraic shifting and strongly edge decomposable complexes - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2008

Algebraic shifting and strongly edge decomposable complexes

Abstract

Let $\Gamma$ be a simplicial complex with $n$ vertices, and let $\Delta (\Gamma)$ be either its exterior algebraic shifted complex or its symmetric algebraic shifted complex. If $\Gamma$ is a simplicial sphere, then it is known that (a) $\Delta (\Gamma)$ is pure and (b) $h$-vector of $\Gamma$ is symmetric. Kalai and Sarkaria conjectured that if $\Gamma$ is a simplicial sphere then its algebraic shifting also satisfies (c) $\Delta (\Gamma) \subset \Delta (C(n,d))$, 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.
Fichier principal
Vignette du fichier
dmAJ0101.pdf (213.76 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01185188 , version 1 (19-08-2015)

Identifiers

Cite

Satoshi Murai. Algebraic shifting and strongly edge decomposable complexes. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.1-12, ⟨10.46298/dmtcs.3652⟩. ⟨hal-01185188⟩

Collections

INSMI TDS-MACS
45 View
398 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More