On the Number of Bh-Sets

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

doi:10.1017/S0963548315000206

On the Number of B_h-Sets

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

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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 language	English
Pages (from-to)	108-129
Number of pages	22
Journal	Combinatorics Probability and Computing
Volume	25
Issue number	1
DOIs	https://doi.org/10.1017/S0963548315000206
State	Published - 1 Jan 2016

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title = "On the Number of Bh-Sets",

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 Erd{\AA}'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.",

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AU - Dellamonica, Domingos

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AU - Lee, Sang June

AU - Rödl, Vojtěch

AU - Samotij, Wojciech

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N2 - 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.

AB - 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.

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On the Number of B_h-Sets

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