Antichain cutsets of strongly connected posets

Details Antichain cutsets of strongly connected posets Antichain cutsets of strongly connected posets

2011-09-26

arxiv.org/abs/1109.5705v2

Mathematics

Combinatorics

12 pages; v2 contains minor fixes for publication

Scientific paper

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.

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