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A new construction for cancellative families of sets. (English) Zbl 0851.05092
Electron. J. Comb. 3, No. 1, Research paper R15, 3 p. (1996); printed version J. Comb. 3, No. 1, 207-209 (1996).
Summary: We say a family, \(H\), of subsets of an \(n\)-element set is cancellative if \(A\cup B= A\cup C\) implies \(B= C\) when \(A, B, C\in H\). We show how to construct cancellative families of sets with \(c2^{.54797n}\) elements. This improves the previous best bound \(c2^{.52832n}\) and falsifies conjectures of Erdös and Katona and of Bollobás.

05D05 Extremal set theory
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