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- W2017307105 abstract "Let F be a Sperner family of subsets of {1,…,m}. Bollobás showed that if A ∈ F ⇒ A = {1,…,m}βA ∈ F, and if the parameters of F are p0,…,pm then ∑i=0[m2 Pim−1i−1 + ∑i=[m2]+1m Pim−1m−i−1 ⩽ 2 Here we generalize this result and prove some analogues of it. A corollary of Bollobás' result is that |F| ⩽ 2([m2]−1m−1). Purdy proved that if A ∈ F ⇒ A ∋ F then |F| ⩽ ([m2]+1m), which implies Bollobás' corollary. We also show that Purdy's result may be deduced from Bollobás' by a short argument. Finally, we give a canonical form for Sperner families which are also pairwise intersecting." @default.
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- W2017307105 date "1979-03-01" @default.
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- W2017307105 title "Some results on sperner families" @default.
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- W2017307105 doi "https://doi.org/10.1016/0097-3165(79)90073-6" @default.
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