Turkish Journal of Mathematics
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.
Keywords
Simplicial complex, Stanley--Reisner ring, shellability, sequentially Cohen--Macaulay
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
