Sizes of Flat Maximal Antichains of Subsets

Abstract This is the second of two papers investigating for which positive integers m there exists a maximal antichain of size m in the Boolean lattice $$B_n$$ B n (the power set of $$[n]:=\{1,2,\dots ,n\}$$ [ n ] : = { 1 , 2 , ⋯ , n } , ordered by inclusion). In the first part, the sizes of maximal...

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Bibliographic Details
Published inOrder (Dordrecht)
Main Authors Griggs, Jerrold R., Kalinowski, Thomas, Leck, Uwe, Roberts, Ian T., Schmitz, Michael
Format Journal Article
LanguageEnglish
Published 27.06.2024
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Summary:Abstract This is the second of two papers investigating for which positive integers m there exists a maximal antichain of size m in the Boolean lattice $$B_n$$ B n (the power set of $$[n]:=\{1,2,\dots ,n\}$$ [ n ] : = { 1 , 2 , ⋯ , n } , ordered by inclusion). In the first part, the sizes of maximal antichains have been characterized. Here we provide an alternative construction with the benefit of showing that almost all sizes of maximal antichains can be obtained using antichains containing only l -sets and $$(l+1)$$ ( l + 1 ) -sets for some l .
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-024-09675-9