Maximal Sidon sets and matroids

5 Maximal Sidon Sets and Matroids

Let X be a subset of an abelian group and a1, . . . , ah, a ′ 1 , . . . , a h a sequence of 2h elements of X such that a1 + · · ·+ah = a ′ 1 + · · ·+a h . The set X is a Sidon set of order h if, after renumbering, ai = a ′ i for i = 1, . . . , h. For k ≤ h, the set X is a generalized Sidon set of order (h, k), if, after renumbering, ai = a ′ i for i = 1, . . . , k. It is proved that if X is a g...

2 00 5 Maximal Sidon Sets and Matroids

Let X be a subset of an abelian group and a1, . . . , ah, a ′ 1 , . . . , a h a sequence of 2h elements of X such that a1 + · · ·+ah = a ′ 1 + · · ·+a h . The set X is a Sidon set of order h if, after renumbering, ai = a ′ i for i = 1, . . . , h. For k ≤ h, the set X is a generalized Sidon set of order (h, k), if, after renumbering, ai = a ′ i for i = 1, . . . , k. It is proved that if X is a g...

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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