The number of B3-sets of a given cardinality

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

doi:https://doi.org/10.1016/j.jcta.2016.03.004

The number of B₃-sets of a given cardinality

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

School of Mathematical Sciences

Tel Aviv University

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

Abstract

A set S of integers is a B₃-set if all the sums of the form a₁+a₂+a₃, with a₁, a₂ and a₃∈S and a₁≤a₂≤a₃, are distinct. We obtain asymptotic bounds for the number of B₃-sets of a given cardinality contained in the interval [n]=(1, . . ., n). We use these results to estimate the maximum size of a B₃-set contained in a typical (random) subset of [n] of a given cardinality. These results confirm conjectures recently put forward by the authors [On the number of B_h-sets, Combin. Probab. Comput. 25 (2016), no. 1, 108-127].

Original language	English
Pages (from-to)	44-76
Number of pages	33
Journal	Journal of Combinatorial Theory. Series A
Volume	142
DOIs	https://doi.org/10.1016/j.jcta.2016.03.004
State	Published - 1 Aug 2016

Keywords

B-set
B-set
Random set
Sidon sequence
Sidon set

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

https://doi.org/10.1016/j.jcta.2016.03.004

Cite this

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title = "The number of B3-sets of a given cardinality",

abstract = "A set S of integers is a B3-set if all the sums of the form a1+a2+a3, with a1, a2 and a3∈S and a1≤a2≤a3, are distinct. We obtain asymptotic bounds for the number of B3-sets of a given cardinality contained in the interval [n]=(1, . . ., n). We use these results to estimate the maximum size of a B3-set contained in a typical (random) subset of [n] of a given cardinality. These results confirm conjectures recently put forward by the authors [On the number of Bh-sets, Combin. Probab. Comput. 25 (2016), no. 1, 108-127].",

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author = "Domingos Dellamonica and Yoshiharu Kohayakawa and Lee, {Sang June} and Vojt{\v e}ch R{\"o}dl and Wojciech Samotij",

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TY - JOUR

T1 - The number of B3-sets of a given cardinality

AU - Dellamonica, Domingos

AU - Kohayakawa, Yoshiharu

AU - Lee, Sang June

AU - Rödl, Vojtěch

AU - Samotij, Wojciech

PY - 2016/8/1

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N2 - A set S of integers is a B3-set if all the sums of the form a1+a2+a3, with a1, a2 and a3∈S and a1≤a2≤a3, are distinct. We obtain asymptotic bounds for the number of B3-sets of a given cardinality contained in the interval [n]=(1, . . ., n). We use these results to estimate the maximum size of a B3-set contained in a typical (random) subset of [n] of a given cardinality. These results confirm conjectures recently put forward by the authors [On the number of Bh-sets, Combin. Probab. Comput. 25 (2016), no. 1, 108-127].

AB - A set S of integers is a B3-set if all the sums of the form a1+a2+a3, with a1, a2 and a3∈S and a1≤a2≤a3, are distinct. We obtain asymptotic bounds for the number of B3-sets of a given cardinality contained in the interval [n]=(1, . . ., n). We use these results to estimate the maximum size of a B3-set contained in a typical (random) subset of [n] of a given cardinality. These results confirm conjectures recently put forward by the authors [On the number of Bh-sets, Combin. Probab. Comput. 25 (2016), no. 1, 108-127].

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KW - Random set

KW - Sidon sequence

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