# 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} }

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

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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 this… Expand

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