%0 Journal Article
%@ 2064-8316
%A  Balogh József
%A  Li Lina
%D 2021
%F acta:73914
%J Acta scientiarum mathematicarum
%K Matematika
%N 1-2
%P 3-21
%T On the number of generalized Sidon sets
%U http://acta.bibl.u-szeged.hu/73914/
%V 87
%X 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.
%Z Bibliogr.: p. 20-21. ; összefoglalás angol nyelven