Abstract
Let 2[n] be the poset of all subsets of {1,...,n} ordered by inclusion. A poset P is said to be contained in a subposet F of 2[n] as a subposet if there exists a subposet P' of F that is isomorphic to P. In this paper we will give an estimate on the size of a maximally sized subposet of 2[n] under the assumption that the subposet does not contain Y(u,v) = ({a1,...,au, b1,...,bv}, {a1< ··· < au, au< b1, au< b2,...,au< bv}) as a subposet.
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Thanh, H.T. An Extremal Problem with Excluded Subposet in the Boolean Lattice. Order 15, 51–57 (1998). https://doi.org/10.1023/A:1006051802267
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DOI: https://doi.org/10.1023/A:1006051802267