Random weighted Sidon sets

Generalized Sidon sets

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. © 2010 Elsevier Inc. All rights reserved. MSC: 11B

Sumsets of Sidon sets

Perfect difference sets constructed from Sidon sets

A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...

The number of Sidon sets and the maximum size of Sidon sets contained in a sparse random set of integers

A set A of non-negative integers is called a Sidon set if all the sums a1+a2, with a1 ≤ a2 and a1, a2 ∈ A, are distinct. A well-known problem on Sidon sets is the determination of the maximum possible size F (n) of a Sidon subset of [n] = {0, 1, . . . , n− 1}. Results of Chowla, Erdős, Singer and Turán from the 1940s give that F (n) = (1 + o(1)) √ n. We study Sidon subsets of sparse random sets...

Arithmetic Characterizations of Sidon Sets

Let G be any discrete Abelian group. We give several arithmetic characterizations of Sidon sets in G. In particular, we show that a set A is a Sidon set iff there is a number 6 > 0 such that any finite subset A of A contains a subset B Q A with |B| > 6\A\ which is quasiindependent, i.e. such that the only relation of the form ]C\eB e x ^ = '̂ with e\ equal to + 1 or 0, is the trivial one. Let G ...