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Linear sets with five distinct differences among any four elements. (English) Zbl 0830.05061
A Sidon set \(S\) (or a \(B_2\)-sequence) is a set of real numbers such that the sums of pairs of numbers from \(S\) are all distinct. The following generalization is proposed: a finite set of real numbers is a \((4, 5)\)-set if every \(4\)-subset determines at least \(5\) distinct differences of pairs. Lower and upper bounds for the size of such a set are derived under the assumption that the set contains a certain Sidon set.

MSC:
05D99 Extremal combinatorics
05C65 Hypergraphs
05C35 Extremal problems in graph theory
11B13 Additive bases, including sumsets
11B25 Arithmetic progressions
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