Some results on Betti numbers of Stanley-Reisner rings

Naoki Terai, Takayuki Hibi

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We study the Betti numbers which appear in a minimal free resolution of the Stanley-Reisner ring k[Δ] = A/IΔ of a simplicial complex Δ over a field k. It is known that the second Betti number of k[Δ] is independent of the base field k. We show that, when the ideal IΔ is generated by square-free monomials of degree two, the third and fourth Betti numbers are also independent of k. On the other hand, we prove that, if the geometric realization of Δ is homeomorphic to either the 3-sphere or the 3-ball, then all the Betti numbers of k[Δ] are independent of the base field k.

Original languageEnglish
Pages (from-to)311-320
Number of pages10
JournalDiscrete Mathematics
Volume157
Issue number1-3
DOIs
Publication statusPublished - Oct 1 1996
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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