Bohr Cluster Points of Sidon Sets

Bohr Cluster Points of Sidon Sets

If there is a Sidon subset of the integers Z which has a member of Z as a cluster point in the Bohr compactification of Z, then there is a Sidon subset of Z which is dense in the Bohr compactification. A weaker result holds for quasiindependent and dissociate subsets of Z. It is a long standing open problem whether Sidon subsets of Z can be dense in the Bohr compactification of Z ([LR]). Yitzha...

Sumsets of 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

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 ...

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...