TY  - JOUR
AV  - restricted
SN  - 2064-8316
JF  - Acta scientiarum mathematicarum
EP  - 21
N1  - Bibliogr.: p. 20-21. ; összefoglalás angol nyelven
IS  - 1-2
ID  - acta73914
A1  -  Balogh József
A1  -  Li Lina
KW  - Matematika
SP  - 3
UR  - http://acta.bibl.u-szeged.hu/73914/
VL  - 87
N2  - 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 Erd?s 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 ?-generalized Sidon set in [n] is a set with at most ? Sidon 4-tuples. One way to extend the problem of Cameron and Erd?s is to estimate the number of ?-generalized Sidon sets in [n]. We show that the number of (n/ log4 n)-generalized Sidon sets in [n] with additional restrictions is 2 ?(?n) In particular, the number of (n/ log5 n)-generalized Sidon sets in [n] is 2 ?(?n) Our approach is based on some variants of the graph container method.
Y1  - 2021///
TI  - On the number of generalized Sidon sets
ER  -