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Let  be the poset generated by the subsets of [] with the inclusion relation and let  be a finite poset. We want to embed  into  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  as , where  denotes the minimal size of the convex hull of a copy of . We discuss both weak and strong (induced) embeddings.

Incomparable Copies of a Poset in the Boolean Lattice