Maximal Betti numbers of Cohen-Macaulay complexes with a given f-vector

Satoshi Murai*, Takayuki Hibi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given the f-vector f = (f 0, f 1, . . .) of a Cohen-Macaulay simplicial complex, it will be proved that there exists a shellable simplicial complex Δ f with f(Δ f ) = f such that, for any Cohen-Macaulay simplicial complex Δ with f(Δ) = f, one has βi(Δ ≤ βi I Δ_ for all i and j, where f(Δ) is the f-vector of Δ and where β ij (I Δ) are graded Betti numbers of the Stanley-Reisner ideal I Δ of Δ.

Original languageEnglish
Pages (from-to)507-512
Number of pages6
JournalArchiv der Mathematik
Issue number6
Publication statusPublished - 2007 Jun
Externally publishedYes


  • Cohen-Macaulay simplicial complex
  • F-vector
  • Graded Betti number
  • H-vector

ASJC Scopus subject areas

  • Mathematics(all)


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