Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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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.

Strong shellability of simplicial complexes

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

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.