Arkiv för Matematik
- Ark. Mat.
- Volume 51, Number 1 (2013), 185-196.
On the h-triangles of sequentially (Sr) simplicial complexes via algebraic shifting
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 Δ be a (d−1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let (hi, j(Δ))0≤j≤i≤d be the h-triangle of Δ and (hi, j(Γ(Δ)))0≤j≤i≤d be the h-triangle of Γ(Δ). In this paper, it is shown that for a Δ being sequentially (Sr) and for every i and j with 0≤j≤i≤r−1, the equality hi, j(Δ)=hi, j(Γ(Δ)) holds true.
Dedicated with gratitude to our teacher and friend Jürgen Herzog on the occasion of his 70th birthday.
Ark. Mat., Volume 51, Number 1 (2013), 185-196.
Received: 12 March 2011
First available in Project Euclid: 31 January 2017
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Pournaki, Mohammad Reza; Seyed Fakhari, Seyed Amin; Yassemi, Siamak. On the h -triangles of sequentially ( S r ) simplicial complexes via algebraic shifting. Ark. Mat. 51 (2013), no. 1, 185--196. doi:10.1007/s11512-011-0160-6. https://projecteuclid.org/euclid.afm/1485907201