On the number of generalized Sidon sets

Balogh József and Li Lina: On the number of generalized Sidon sets. In: Acta scientiarum mathematicarum, (87) 1-2. pp. 3-21. (2021)

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Abstract

A set A of nonnegative integers is called a Sidon set if there is no Sidon 4-tuple, i.e., (a, b, c, d) in A with a + b = c + d and {a, b} ∩ {c, d} = ∅. Cameron and Erdős proposed the problem of determining the number of Sidon sets in [n]. Results of Kohayakawa, Lee, Rödl and Samotij, and Saxton and Thomason have established that the number of Sidon sets is between 2 (1.16+o(1))√n and 2 (6.442+o(1))√n . An α-generalized Sidon set in [n] is a set with at most α Sidon 4-tuples. One way to extend the problem of Cameron and Erdős is to estimate the number of α-generalized Sidon sets in [n]. We show that the number of (n/ log4 n)-generalized Sidon sets in [n] with additional restrictions is 2 Θ(√n) In particular, the number of (n/ log5 n)-generalized Sidon sets in [n] is 2 Θ(√n) Our approach is based on some variants of the graph container method.

Item Type: Article
Heading title: Algebra
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2021
Volume: 87
Number: 1-2
ISSN: 2064-8316
Page Range: pp. 3-21
Language: English
Related URLs: http://acta.bibl.u-szeged.hu/73791/
DOI: 10.14232/actasm-018-777-z
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 20-21. ; összefoglalás angol nyelven
Date Deposited: 2021. Nov. 15. 15:12
Last Modified: 2021. Nov. 15. 15:12
URI: http://acta.bibl.u-szeged.hu/id/eprint/73914

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