Corpus ID: 232417382

# An upper bound on the size of Sidon sets

```@article{Balogh2021AnUB,
title={An upper bound on the size of Sidon sets},
author={J{\'o}zsef Balogh and Zolt{\'a}n F{\"u}redi and Souktik Roy},
journal={ArXiv},
year={2021},
volume={abs/2103.15850}
}```
• Published 2021
• Computer Science, Mathematics
• ArXiv
In this entry point into the subject, combining two elementary proofs, we decrease the gap between the upper and lower bounds by 0.2% in a classical combinatorial number theory problem. We show that the maximum size of a Sidon set of {1, 2, . . . , n} is at most √n+ 0.998n for sufficiently large n. 1. History In 1932 S. Sidon asked a question of a fellow student P. Erdős. Their advisor was L. Fejér, an outstanding mathematician (cf. Fejér kernel) working on summability of infinite series, who… Expand
1 Citations
Upper and lower bounds on the size of \$B_k[g]\$ sets
• Mathematics
• 2021
A subset A of the integers is a Bk[g] set if the number of multisets from A that sum to any fixed integer is at most g. Let Fk,g(n) denote the maximum size of a Bk[g] set in {1, . . . , n}. In thisExpand

#### References

SHOWING 1-10 OF 29 REFERENCES
SIDON SETS IN N
We study finite and infinite Sidon sets in N. The additive energy of two sets is used to obtain new upper bounds for the cardinalities of finite Sidon subsets of some sets as well as to provide shortExpand
• Mathematics
• 2018
We show that the de Bruijn-Erdős condition for the error term in their improvement of Fekete's Lemma is not only sufficient but also necessary in the following strong sense. Suppose that given aExpand
g-Golomb Rulers
• Mathematics
• 2015
A set of positive integers A is called a g-Golomb ruler if the difference between two distinct elements of A is repeated at most g times. This definition is a generalization of the Golomb ruler (g =Expand
Combinatorial problems in finite fields and Sidon sets
We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solvability of some equations and the distribution of theirExpand
What are dense Sidon subsets
• 2012
Sidon sets in N d
• J. Combin. Theory Ser. A
• 2010
A note on weak Sidon sequences
• P. Kayll
• Computer Science, Mathematics
• Discret. Math.
• 2005
The present proof improves Ruzsa's bound by decreasing the implicit constant, essentially from 4 to 3 . Expand
A Complete Annotated Bibliography of Work Related to Sidon Sequences
A Sidon sequence is a sequence of integers \$a_1 < a_2 < \cdots\$ with the property that the sums \$a_i + a_j\$ \$(i\le j)\$ are distinct. This work contains a survey of Sidon sequences and theirExpand