Antichain cutsets of strongly connected posets
Combinatorics
2013-06-27 v2
Abstract
Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a corollary, we get such a characterization for semimodular lattices, supersolvable lattices, Bruhat orders, locally shellable lattices, and many more. We also consider a generalization to strongly connected hypergraphs having finite edges.
Keywords
Cite
@article{arxiv.1109.5705,
title = {Antichain cutsets of strongly connected posets},
author = {Stephan Foldes and Russ Woodroofe},
journal= {arXiv preprint arXiv:1109.5705},
year = {2013}
}
Comments
12 pages; v2 contains minor fixes for publication