Incomparable Copies of a Poset in the Boolean Lattice

Katona, Gyula and Nagy, D.T. (2015) Incomparable Copies of a Poset in the Boolean Lattice. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS. ISSN 0167-8094

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Abstract

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

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