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arXiv · 2512.14826

Antichain cutsets in real-ranked lattices

Stephan Foldes·Russ Woodroofe
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Abstract

We show that in a rank supersolvable lattice that is graded by a bounded real interval, any antichain cutset is a level set for some appropriately constructed grading. As a consequence, given an antichain cutset in any of the measurable Boolean lattice, a continuous partition lattice, or a continuous projective geometry, we may find a grading in which the cutset is a level set.

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Stephan Foldes, Russ Woodroofe. 2026-03-01. Antichain cutsets in real-ranked lattices. https://arxiv.org/abs/2512.14826

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