Abstract
The Boolean lattice 2[n] is the power set of [n] ordered by inclusion. If c is a positive integer, a c-partition of a poset is a chain partition, where all but at most one of the chains have size c. We prove that if n=Ω(c2), then 2[n] has a c-partition. This improves a theorem of Lonc.We also prove a generalization of this result. If c is a positive integer and P is a poset whose comparability graph is connected, then Pn has a c-partition if n is sufficiently large.
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