Elsevier

Discrete Applied Mathematics

Volume 169, 31 May 2014, Pages 219-224
Discrete Applied Mathematics

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Forbidding a set difference of size 1

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Abstract

How large can a family AP[n] be if it does not contain A,B with |AB|=1? Our aim in this paper is to show that any such family has size at most 2+o(1)n(nn/2). This is tight up to a multiplicative constant of 2. We also obtain similar results for families AP[n] with |AB|k, showing that they satisfy |A|Cknk(nn/2), where Ck is a constant depending only on k.

Keywords

Sperner family
Antichain
Extremal set theory

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