J. Korean Math. Soc. 2019; 56(6): 1613-1639
Online first article July 17, 2019 Printed November 1, 2019
https://doi.org/10.4134/JKMS.j180831
Copyright © The Korean Mathematical Society.
Jin Guo, Yi-Huang Shen, Tongsuo Wu
Hainan University; University of Science and Technology of China; Shanghai Jiaotong University
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
Supported by: Supported by the National Natural Science Foundation of China (Grant No. 11201445, 11601108, 11526065 and 11271250), the Fundamental Research Funds for the Central Universities, and the Young Talents’ Sci ence and Technology Innovation Project of Hainan Association for Science and Technology (Grant No. QCXM201806), NSF of Shanghai 19ZR1424100.
2018; 55(6): 1381-1388
2013; 50(3): 543-555
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