In 2010, Cilleruelo, Ruzsa, and Vinuesa established a surprising connection between the maximum possible size of generalized Sidon set in first $N$ natural numbers optimal constant an “analogous” problem concerning nonnegative-valued func

Sidon sets are those sets such that the sums of two of its elements never coincide. They go back to the 30s when Sidon asked for the maximal size of a subset of consecutive integers with that property. This question is now answered in a satisfactory way. Their natural generalization, called B2[g] sets and defined by the fact that there are at most g ways (up to reordering the summands) to repre...

INTRODUCTION Sixty years ago Sidon [7] asked, in the course of some investigations of Fourier series, for a sequence a1 < a2... for which the sums ai + aj are all distinct and for which ak tends to infinity as slowly as possible. Sidon called these sequences, B2 sequences. The greedly algorithm gives ak ¿ k and this was the best result until Atjai, Komlos and Szemeredi [1] found a B2 sequence s...