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- W2951308385 abstract "We prove a supersaturation-type extension of both Sperner's Theorem (1928) and its generalization by Erdos (1945) to k-chains. Our result implies that a largest family whose size is x more than the size of a largest k-chain free family and that contains the minimum number of k-chains is the family formed by taking the middle (k-1) rows of the Boolean lattice and x elements from the k-th middle row. We prove our result using the symmetric chain decomposition method of de Bruijn, van Ebbenhorst Tengbergen, and Kruyswijk (1951)." @default.
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- W2951308385 date "2014-05-20" @default.
- W2951308385 modified "2023-10-16" @default.
- W2951308385 title "Supersaturation in the Boolean lattice" @default.
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