## Abstract

A set A of positive integers is a Bh-set if all the sums of the form a_{1} +.. + ah, with a_{1},.., ah A and a_{1}.. 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 language | English |
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Pages (from-to) | 108-129 |

Number of pages | 22 |

Journal | Combinatorics Probability and Computing |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2016 |

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