Turkish Journal of Mathematics
Article Title
Shellability of simplicial complexes and simplicial complexes with the free vertex property
DOI
10.3906/mat-1411-54
Abstract
To a simplicial complex $\Delta$, we associate a square-free monomial ideal $\mathcal{F}(\Delta)$ in the polynomial ring generated by its facet over a field. Furthermore, we could consider $\mathcal{F}(\Delta)$ as the Stanley--Reisner ideal of another simplicial complex $\delta_{N}(\mathcal{F}(\Delta))$ from facet ideal theory and Stanley--Reisner theory. In this paper, we determine what families of simplicial complexes $\Delta$ have the property that their Stanley--Reisner complexes $\delta_{N}(\mathcal{F}(\Delta))$ are shellable. Furthermore, we show that the simplicial complex with the free vertex property is sequentially Cohen--Macaulay. This result gives a new proof for a result of Faridi on the sequentially Cohen--Macaulayness of simplicial forests.
First Page
181
Last Page
190
Recommended Citation
ZHU, GUANGJUN
(2016)
"Shellability of simplicial complexes and simplicial complexes with the free vertex property,"
Turkish Journal of Mathematics: Vol. 40:
No.
1, Article 16.
https://doi.org/10.3906/mat-1411-54
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss1/16
