ON SIDON SETS IN A RANDOM SET OF VECTORS

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...

On Multiplicative Sidon Sets

Fix integers b > a ≥ 1 with g := gcd(a, b). A set S ⊆ N is {a, b}-multiplicative if ax 6= by for all x, y ∈ S. For all n, we determine an {a, b}-multiplicative set with maximum cardinality in [n], and conclude that the maximum density of an {a, b}-multiplicative set is b b+g . Erdős [2, 3, 4] defined a set S ⊆ N to be multiplicative Sidon1 if ab = cd implies {a, b} = {c, d} for all a, b, c, d ∈...

On Uniformly Approximable Sidon Sets

Let G be a compact abelian group and let T be the character group of G. Suppose £ is a subset of T. A trigonometric polynomial f on G is said to be an ^-polynomial if its Fourier transform / vanishes off E. The set E is said to be a Sidon set if there is a positive number B such that 2^xeb |/(X)| á-B||/||u for all E-polynomials /; here, ||/||„ = sup{ |/(x)| : xEG}. In this note we shall discuss...

Sumsets of Sidon sets

Sidon Sets in N

We study finite and infinite Sidon sets in N. The additive energy of two sets is used to obtain new upper bounds for the cardinalities of finite Sidon subsets of some sets as well as to provide short proofs of already known results. We also disprove a conjecture of Lindstrom on the largest Sidon set in [1, N ]× [1, N ] and relate it to a known conjecture of Vinogradov concerning the size of the...