Antichain cutsets in real-ranked lattices
Combinatorics
2026-03-03 v2
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.
Keywords
Cite
@article{arxiv.2512.14826,
title = {Antichain cutsets in real-ranked lattices},
author = {Stephan Foldes and Russ Woodroofe},
journal= {arXiv preprint arXiv:2512.14826},
year = {2026}
}
Comments
12 pages, 1 figure; v2 has minor changes before submission