H-vectors of simplicial complexes with Serre's conditions

Satoshi Murai*, Naoki Terai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


We study h-vectors of simplicial complexes which satisfy Serre's condition (Sr). Let r be a positive integer. We say that a simplicial complex △ satisfies Serre's condition (Sr) if H̃ i(lk (F);K) = 0 for all F ∈ △ and for all i < min{r-1, dim lk (F)}, where lk (F) is the link of △ with respect to F and where H̃i(△;K) is the reduced homology groups of △ over a field K. The main result of this paper is that if △ satisfies Serre's condition (Sr) then (i) hk(△) is non-negative for k = 0, 1, . . ., r and (ii) ∑k≥r hk(△) is non-negative.

Original languageEnglish
Pages (from-to)1015-1028
Number of pages14
JournalMathematical Research Letters
Issue number6
Publication statusPublished - 2009 Nov
Externally publishedYes


  • Graded Betti numbers
  • H-vectors
  • Serre's conditions
  • Stanley-Reisner rings

ASJC Scopus subject areas

  • Mathematics(all)


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