Additive and multiplicative Sidon 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 ∈...

Additive and Multiplicative Structures of C ? - Sets

It is known that for an IP? set A in (N,+) and a sequence hxnin=1 in N, there exists a sum subsystem hynin=1 of hxnin=1 such that FS(hynin=1) [ FP (hynin=1) ✓ A. Similar types of results have also been proved for central? sets where the sequences have been considered from the class of minimal sequences. In this present work, we shall prove some analogous results for C?-sets for a more general c...

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

Sidon sets and Riesz products

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