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On the Number of Bh-Sets
Published online by Cambridge University Press: 16 September 2015
Abstract
A set A of positive integers is a Bh-set if all the 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 Erdős (1990) in the context of Bh-sets. We also use these results to estimate the maximum size of a Bh-sets contained in a typical (random) subset of [n] with a given cardinality.
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- Combinatorics, Probability and Computing , Volume 25 , Issue 1: Oberwolfach Special Issue Part 2 , January 2016 , pp. 108 - 129
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- Copyright © Cambridge University Press 2015
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