Uniform chain decompositions and applications

The Boolean lattice 2[n] is the family of all subsets of [n]={1,…,n} ordered by inclusion, and a chain is a family of pairwise comparable elements of 2[n]. Let s=2n/n⌊n/2⌋, which is the average size of a chain in a minimal chain decomposition of 2[n]. We prove that 2[n] can be partitioned into n⌊n/2...

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Veröffentlicht in:	Random structures & algorithms 2022-03, Vol.60 (2), p.261-286
Hauptverfasser:	Sudakov, Benny, Tomon, István, Wagner, Adam Zsolt
Format:	Artikel
Sprache:	eng
Schlagworte:	antichain Boolean algebra Boolean lattice chain decomposition Chains container method Decomposition Furedi's conjecture Set theory
Online-Zugang:	Volltext
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