On the Number of Bh-Sets

Domingos Dellamonica, Yoshiharu Kohayakawa, Sang June Lee, Vojtěch Rödl and Wojciech Samotij

A set A of positive integers is a Bh-set if all sums of the form a1 + ··· + ah, with a1,...,ah ∈ A and a1 ··· ah, are distinct. We provide asymptotic bounds for the number of Bh-sets of a given cardinality contained in the interval [n] = {1,...,n}. As a consequence of our results, we address a problem of Cameron and Erd˝os (1990) in the context of Bh-sets.
We also use these results to estimate the maximum size of a Bh-set contained in a typical (random) subset of [n] with a given cardinality.

The whole paper is available here.



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