Sperner theory in a difference of Boolean lattices

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Consider any sets x ⊆ y ⊆ {1,...,n}. Remove the interval [x,y] = {z ⊆ y|x ⊆ z} from the Boolean lattice of all subsets of {1,...,n}. We show that the resulting poset, ordered by inclusion, has a nested chain decomposition and has the normalized matching property. We also classify the largest antichains in this poset. This generalizes results of Griggs, who resolved these questions in the special case x = .

Original languageEnglish (US)
Pages (from-to)501-512
Number of pages12
JournalDiscrete Mathematics
Issue number2-3
StatePublished - Nov 28 2002
Externally publishedYes
EventKleitman and Combinatorics: A Celebration - Cambridge, MA, United States
Duration: Aug 16 1990Aug 18 1990


  • Antichains
  • Boolean lattice
  • Chain decompositions
  • Lym property
  • Normalized matching property


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