Incomparable copies of a poset in the Boolean lattice

2013/09/27 by Gyula O. H. Katona, Katona, Gyula O. H., Dániel T. Nagy +1
Computer Science · Mathematics · #05D05 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05D05 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1309.7379

8 pages

arxiv created 2013/09/27 · openalex publication_date 2013/09/27 · arxiv updated 2013/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B_n be the poset generated by the subsets of [n] with the inclusion as relation and let P be a finite poset. We want to embed P into B_n as many times as possible such that the subsets in different copies are incomparable. The maximum number of such embeddings is asymptotically determined for all finite posets P as (n \choose \lfloor n/2\rfloor)/(M(P)), where M(P) denotes the minimal size of the convex hull of a copy of P. We discuss both weak and strong (induced) embeddings.

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