On the h-triangles of sequentially (Sr) simplicial complexes via algebraic shifting

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 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.