Incomparable copies of a poset in the Boolean lattice
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Incomparable copies of a poset in the Boolean lattice
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Incomparable copies of a poset in the Boolean lattice Gyula O.H. Katona∗ and Dániel T. Nagy†
arXiv:1309.7379v1 [math.CO] 27 Sep 2013
October 1, 2013
Abstract Let Bn 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 Bn as many times as possible such that the subsets in different copies are incomparable. The maximum number of such embeddings is asymptotically determined n (⌊n/2⌋ ) for all finite posets P as M , where M (P ) denotes the minimal size of the convex hull of a copy (P ) of P . We discuss both weak and strong (induced) embeddings.
1
Introduction
Definition Let Bn be the Boolean lattice, the poset generated by the subsets of [n] with the inclusion as relation and P be a finite poset with the relation
