English

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