Abstract
LetB n(s, t) denote the partially ordered set consisting of alls-subsets andt-subsets of ann-element underlying set where these sets are ordered by inclusion. Answering a question of Trotter we prove that dim(B n(k, n−k))=n−2 for 3⩽k<(1/7)n 1/3. The proof uses extremal hypergraph theory.
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Füredi, Z. The order dimension of two levels of the Boolean lattice. Order 11, 15–28 (1994). https://doi.org/10.1007/BF01462226
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DOI: https://doi.org/10.1007/BF01462226