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“School of Mathematics”

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Paper   IPM / M / 11812
School of Mathematics
  Title:   On the h-vector of a simplicial complex with Serre's condition
  Author(s): 
1.  M. R. Pournaki
2.  S. Yassemi (Joint with A. Goodarzi and S. A. Seyed Fakhari)
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Vol.:  216
  Year:  2012
  Pages:   91-94
  Supported by:  IPM
  Abstract:
Let ∆ be a (d−1)-dimensional simplicial complex and let h(∆) = (h0,h1,…,hd) be its h-vector. A recent result of Murai and Terai guarantees that if ∆ satisfies Serre's condition (Sr), then (h0,h1,…,hr) is an M-vector and hr+hr+1+…+hd is nonnegative. In this article, we extend the result of Murai and Terai by giving r extra necessary conditions. More precisely, we prove that if ∆ satisfies Serre's condition (Sr), then ((i) || (i))hr+((i+1) || (i))hr+1+…+((i+dr) || (i))hd, 0 ≤ ird, are all nonnegative.


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