Generalized Sidon sets
Javier Cilleruelo, Imre Z. Ruzsa, Carlos Vinuesa

TL;DR
This paper provides precise asymptotic estimates for the size of residue class sets with bounded representation functions and extends these results to integer sets, addressing a longstanding question by Simon Sidon.
Contribution
It introduces sharp asymptotic bounds for generalized Sidon sets and applies these to solve an open problem related to sets of integers.
Findings
Asymptotic estimates for residue class sets
Extension of results to integer sets
Resolution of an old question of Simon Sidon
Abstract
We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Analytic Number Theory Research · Advanced Topology and Set Theory
