Shelling the Coset Poset
群论
2011-01-27 v4 组合数学
摘要
It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen-Macaulay order complex in exactly the same conditions. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and of minimal finite simple groups.
引用
@article{arxiv.math/0306346,
title = {Shelling the Coset Poset},
author = {Russ Woodroofe},
journal= {arXiv preprint arXiv:math/0306346},
year = {2011}
}
备注
14 pages, 3 figures; Improved exposition of Lemma 4.1, other minor fixes. Submitted to Journal of Combinatorial Theory, Series A