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arXiv · 1109.5705

Antichain cutsets of strongly connected posets

Stephan Foldes·Russ Woodroofe
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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.

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Stephan Foldes, Russ Woodroofe. 2012-02-17. Antichain cutsets of strongly connected posets. https://doi.org/10.1007/s11083-012-9248-2

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