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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.

##### MSC:
 05D05 Extremal set theory
##### Keywords:
cancellative families
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