## 19 Citations

Gaps in dense sidon sets

- Mathematics
- 2000

We prove that if A ⊂ [1, N ] is a Sidon set with N1/2−L elements, then any interval I ⊂ [1, N ] of length cN contains c|A|+EI elements of A, with |EI | ≤ 52N(1+ c1/2N1/8)(1+L + N−1/8), L+ = max{0,…

On Sum Sets of Sidon Sets, 1.

- Mathematics
- 1994

It is proved that there is no Sidon set selected from {1, 2, …,N} whose sum set containsc1N1/2 consecutive integers, but it may containc2N1/3 consecutive integers. Moreover, it is shown that a finite…

On sum sets of sidon sets, II

- Mathematics
- 1995

It is proved that there is no Sidon set selected from {1, 2, …,N} whose sum set containsc1N1/2 consecutive integers, but it may containc2N1/3 consecutive integers. Moreover, it is shown that a finite…

Random Sidon Sequences

- Mathematics
- 1999

A subset A of the set [n] = {1, 2,..., n}, \A\ = k, is said to form a Sidon (or B-h) sequence, h greater than or equal to 2, if each of the sums a(1) + a(2) +...+ a(h), a(1) less than or equal to…

SIDON SETS WITH SMALL GAPS

- Mathematics
- 1995

Let N denote the set of positive integers. A set A⊂N is called a Sidon set if the sums a + a (a, a∊A) are all distinct. For background on Sidon sets, we refer to [6]. For additional recent results…

B h sequences

- Mathematics
- 1996

Let A be a set (finite or infinite) of natural numbers, and let a i denote a generic element of A. We say that A is a B h sequence if the sums of the form a 1 + … + a h (a 1 ≤ … ≤ a h ) are all…

Well Distribution of Sidon Sets in Residue Classes

- Mathematics
- 1998

Abstract A set A of non-negative integers is a Sidon set if the sums a + b ( a , b ∈ A , a ⩽ b ) are distinct. Assume that a ⊆[1, n ] and that | A |=(1+ o (1)) n 1/2 . Let m ⩾2 be an integer. In…

INTEGER SETS HAVING THE MAXIMUM NUMBER OF DISTINCT DIFFERENCES

- Mathematics
- 2007

In this paper we study the function D(k,n) which is the maximum of |A ! A| = ! {a ! b : a,b " A} ! over all k-subsets A of {0,...,n}. We prove that for any fixed real c # 0 and any function k(n) = (c…

Extremal Sidon sets are Fourier uniform, with applications to partition regularity

- Mathematics
- 2021

Generalising results of Erdős-Freud and Lindström, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing…

Continuous Ramsey Theory and Sidon Sets

- Mathematics
- 2002

A symmetric subset of the reals is one that remains invariant under some reflection x --> c-x. Given 0 D(x), then there exists a subset of [0,1] with measure x that does not contain a symmetric…

## References

On a problem of sidon in additive number theory, and on some related problems

- Mathematics
- 1941

To the memory of S. Sidon. Let 0 < a, < a,. .. be an infinite sequence of positive integers. Denote by f(n) the number of solutions of n=a i +a;. About twenty years ago, SIDON 1) raised the question…