Saturated simplicial complexes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:109

Article

Mnukhin, VB ; Siemons, J

关键词: modular homology;    simplicial complex;    Cohen-Macaulay poset;    shellability;    p-rank;    rank-selection;    order complex;    geometric lattice;    Steinberg representation;    shellable posets and Cohen-Macaulay posets buildings and the geometry of diagrams;   

DOI  :  10.1016/j.jcta.2004.08.003

来源: Elsevier

【 摘 要 】

Among shellable complexes a certain class has maximal modular homology, and these are the so-called saturated complexes. We extend the notion of saturation to arbitrary pure complexes and give a survey of their properties. It is shown that saturated complexes can be characterized via the p-rank of incidence matrices and via the structure of links. We show that rank-selected subcomplexes of saturated complexes are also saturated, and that order complexes of geometric lattices are saturated. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free