Computation of Betti numbers of monomial ideals associated with stacked polytopes

Naoki Terai, Takayuki Hibi

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Let P(v, d) be a stacked d-polytope with v vertices, Δ(P(v,d)) the boundary complex of P(v,d), and k[Δ(P(v,d))] = A/IΔ(P(v,d)) the Stanley-Reisner ring of Δ(P(v,d)) over a field k. We compute the Betti numbers which appear in a minimal free resolution of k[Δ(P(v,d))] over A, and show that every Betti number depends only on v and d and is independent of the base field k. We also show that the Betti number sequences above are unimodal.

Original languageEnglish
Pages (from-to)447-453
Number of pages7
JournalManuscripta Mathematica
Volume92
Issue number4
DOIs
Publication statusPublished - Apr 1997
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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