Sperner theory in a difference of Boolean lattices

Mark J. Logan

doi:10.1016/S0012-365X(02)00509-5

Sperner theory in a difference of Boolean lattices

Mark J. Logan

Research output: Contribution to journal › Conference article › peer-review

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Abstract

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 language	English (US)
Pages (from-to)	501-512
Number of pages	12
Journal	Discrete Mathematics
Volume	257
Issue number	2-3
DOIs	https://doi.org/10.1016/S0012-365X(02)00509-5
State	Published - Nov 28 2002
Externally published	Yes
Event	Kleitman and Combinatorics: A Celebration - Cambridge, MA, United States Duration: Aug 16 1990 → Aug 18 1990

Keywords

Antichains
Boolean lattice
Chain decompositions
Lym property
Normalized matching property

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AB - 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 = .

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KW - Boolean lattice

KW - Chain decompositions

KW - Lym property

KW - Normalized matching property

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T2 - Kleitman and Combinatorics: A Celebration

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ER -

Sperner theory in a difference of Boolean lattices

Abstract

Keywords

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