On the Number ofBh-Sets

Abstract

A setAof positive integers is aBh-setif all the sums of the forma1+ . . . +ah, witha1,. . .,ah∈Aanda1⩽ . . . ⩽ah, are distinct. We provide asymptotic bounds for the number ofBh-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 Erdős (1990) in the context ofBh-sets. We also use these results to estimate the maximum size of aBh-sets contained in a typical (random) subset of [n] with a given cardinality.