Packing Posets in the Boolean Lattice

2013/09/25 by Andrew P. Dove, Dove, Andrew P., Jerrold R. Griggs +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1309.6686

arxiv created 2013/09/25 · arxiv updated 2013/09/27

Abstract

We are interested in maximizing the number of pairwise unrelated copies of a poset P in the family of all subsets of [n]. We prove that for any P the maximum number of unrelated copies of P is asymptotic to a constant times the largest binomial coefficient. Moreover, the constant has the form (1)/(c(P)), where c(P) is the size of the smallest convex closure over all embeddings of P into the Boolean lattice.

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