On the number of generalized Sidon sets
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...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
|
| Sorozat: | Acta scientiarum mathematicarum
87 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-018-777-z |
| Online Access: | http://acta.bibl.u-szeged.hu/73914 |
| LEADER | 01574nab a2200217 i 4500 | ||
|---|---|---|---|
| 001 | acta73914 | ||
| 005 | 20211115151235.0 | ||
| 008 | 211115s2021 hu o 0|| eng d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-018-777-z |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Balogh József | |
| 245 | 1 | 3 | |a On the number of generalized Sidon sets |h [elektronikus dokumentum] / |c Balogh József |
| 260 | |c 2021 | ||
| 300 | |a 3-21 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 87 No. 1-2 | |
| 520 | 3 | |a 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. | |
| 695 | |a Matematika | ||
| 700 | 0 | 1 | |a Li Lina |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/73914/1/math_087_numb_001-002_003-021.pdf |z Dokumentum-elérés |