Generic initial ideals and exterior algebraic shifting of the join of simplicial complexes
| dc.creator | Murai, Satoshi | |
| dc.date | 2005-06-15 | |
| dc.date | 2006-12-14 | |
| dc.date.accessioned | 2026-07-07T07:34:32Z | |
| dc.date.available | 2026-07-07T07:34:32Z | |
| dc.description | In this paper, the relation between algebraic shifting and join which was conjectured by Eran Nevo will be proved. Let $σ$ and $τ$ be simplicial complexes and $σ* τ$ their join. Let $J_σ$ be the exterior face ideal of $σ$ and $Δ(σ)$ the exterior algebraic shifted complex of $σ$. Assume that $σ* τ$ is a simplicial complex on $[n]=\{1,2,...,n\}$. For any $d$-subset $S \subset [n]$, let $m_{\preceq_{rev} S}(σ)$ denote the number of $d$-subsets $R \in σ$ which is equal to or smaller than $S$ w.r.t. the reverse lexicographic order. We will prove that $m_{\preceq_{rev} S}(Δ({σ* τ}))\geq m_{\preceq_{rev} S}(Δ({Δ(σ)} * {Δ(τ)}))$ for all $S \subset [n]$. To prove this fact, we also prove that $m_{\preceq_{rev} S}(Δ(σ))\geq m_{\preceq_{rev} S}(Δ({Δ_ϕ(σ)}))$ for all $S\subset [n]$ and for all non-singular matrices $ϕ$, where $Δ_ϕ(σ)$ is the simplicial complex defined by $J_{Δ_ϕ(σ)}=\init(ϕ(J_σ))$. | |
| dc.description | Improve presentations, 8 pages, to appear in Ark. Mat | |
| dc.identifier | https://arxiv.org/abs/math/0506298 | |
| dc.identifier | http://arxiv.org/abs/math/0506298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119799 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F55; 05E99 | |
| dc.title | Generic initial ideals and exterior algebraic shifting of the join of simplicial complexes | |
| dc.type | text |