A flat antichain is a collection of incomparable subsets of a finite ground set, such that |B|−|C|≤1 for every two members B, C. Using Lieby’s results, we prove the Flat Antichain Conjecture, which says that for any antichain there exists a flat antichain having the same cardinality and average set size.
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Kisvölcsey, Á. Flattening Antichains. Combinatorica 26, 65–82 (2006). https://doi.org/10.1007/s00493-006-0005-2
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DOI: https://doi.org/10.1007/s00493-006-0005-2