Maximal antichains of subsets II: Constructions

06/04/2021

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by   Jerrold R. Griggs, et al.

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This is the second in a sequence of three papers investigating the question for which positive integers m there exists a maximal antichain of size m in the Boolean lattice B_n (the power set of [n]:={1,2,…,n}, ordered by inclusion). In the previous paper we characterized those m between n⌈ n/2⌉-⌈ n/2⌉^2 and the maximum size n⌈ n/2 ⌉ that are not sizes of maximal antichains. In this paper we show that all smaller m are sizes of maximal antichains.