On the Number of Bh-Sets

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

Research output: Contribution to journalArticlepeer-review

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 ErdÅ's (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.

Original languageEnglish
Pages (from-to)108-129
Number of pages22
JournalCombinatorics Probability and Computing
Volume25
Issue number1
DOIs
StatePublished - 1 Jan 2016

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