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Paper   IPM / M / 12016
School of Mathematics
  Title:   On the h-triangles of sequentially (Sr) simplicial complexes via algebraic shifting
  Author(s): 
1.  M. R. Pournaki
2.  S. Yassemi (Joint with S. A. Seyed Fakhari)
  Status:   Published
  Journal: Ark. Mat.
  Vol.:  51
  Year:  2013
  Pages:   185-196
  Supported by:  IPM
  Abstract:
Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially (Sr) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen-Macaulay and satisfying Serre's condition (Sr). Let ∆ be a (d−1)-dimensional simplicial complex with Γ(∆) as its algebraic shifting. Also let (hi,j(∆))0 ≤ jid be the h-triangle of ∆ and (hi,j(Γ(∆)))0 ≤ jid be the h-triangle of Γ(∆). In this paper, it is shown that for a ∆ being sequentially (Sr) and for every i and j with 0 ≤ jir−1, the equality hi,j(∆) = hi,j(Γ(∆)) holds true.


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