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 :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| 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 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 3-21 |
| ISSN: | 2064-8316 |