Antichain cutsets of strongly connected posets
arXiv:1109.5705 · doi:10.1007/s11083-012-9248-2
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.
arXiv comment12 pages; v2 contains minor fixes for publication