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http://dx.doi.org/10.4134/JKMS.j180831

STRONG SHELLABILITY OF SIMPLICIAL COMPLEXES  

Guo, Jin (College of Information Science and Technology Hainan University)
Shen, Yi-Huang (Wu Wen-Tsun Key Laboratory of Mathematics of CAS and School of Mathematical Sciences University of Science and Technology of China)
Wu, Tongsuo (College of Mathematical Sciences Shanghai Jiaotong University)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.6, 2019 , pp. 1613-1639 More about this Journal
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;
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