# MathSciDoc: An Archive for Mathematician ∫

#### mathscidoc:1701.01018

Arkiv for Matematik, 51, (1), 185-196, 2011.3
Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially (\$S\$_{\$r\$}) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen–Macaulay and satisfying Serre’s condition (\$S\$_{\$r\$}). Let Δ be a (\$d\$−1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let (\$h\$_{\$i\$,\$j\$}(Δ))_{0≤\$j\$≤\$i\$≤\$d\$}be the\$h\$-triangle of Δ and (\$h\$_{\$i\$,\$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 (\$S\$_{\$r\$}) and for every\$i\$and\$j\$with 0≤\$j\$≤\$i\$≤\$r\$−1, the equality\$h\$_{\$i\$,\$j\$}(Δ)=\$h\$_{\$i\$,\$j\$}(Γ(Δ)) holds true.
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```@inproceedings{mohammad2011on,
title={On the\$h\$-triangles of sequentially (\$S\$_{\$r\$}) simplicial complexes via algebraic shifting},
author={Mohammad Reza Pournaki, Seyed Amin Seyed Fakhari, and Siamak Yassemi},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634739633037},
booktitle={Arkiv for Matematik},
volume={51},
number={1},
pages={185-196},
year={2011},
}
```
Mohammad Reza Pournaki, Seyed Amin Seyed Fakhari, and Siamak Yassemi. On the\$h\$-triangles of sequentially (\$S\$_{\$r\$}) simplicial complexes via algebraic shifting. 2011. Vol. 51. In Arkiv for Matematik. pp.185-196. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634739633037.
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