Strong shellability of simplicial complexes
J. Korean Math. Soc. 2019 Vol. 56, No. 6, 1613-1639
Published online November 1, 2019
Jin Guo, Yi-Huang Shen, Tongsuo Wu
Hainan University; University of Science and Technology of China; Shanghai Jiaotong University
Abstract : Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure strongly shellable complexes. Meanwhile, pure strongly shellable complexes can be characterized by the corresponding codimension one graphs. In addition, we show that the facet ideals of pure strongly shellable complexes have linear quotients.
Keywords : simplicial complex, strongly shellable, linear quotients, Cohen-Macaulayness
MSC numbers : 13F55, 05E45, 13F20
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