Supersaturation in the Boolean lattice
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Publication date
2014-05-14
Authors
Dove, A.P.
Griggs, J.R.
Kang, Ross
Sereni, Jean-Sébastien
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Abstract
We seek families of subsets of an n-set of given size that contain the fewest k-chains. We prove a “supersaturation-type” extension of both Sperner’s Theorem (1928) and its generalization by Erd˝os (1945). Erd˝os showed that a largest k-chain free family in the Boolean lattice is formed by taking all subsets of the (k
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Dove, A P, Griggs, J R, Kang, R & Sereni, J-S 2014, 'Supersaturation in the Boolean lattice', Integers : electronic journal of combinatorial number theory, vol. 14A, A4, pp. 1-7.