Linear sets with five distinct differences among any four elements. (English) Zbl 0830.05061

Gyárfás, András; Lehel, Jenö

J. Comb. Theory, Ser. B 64, No. 1, 108-118 (1995).

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.

Reviewer: V.D.Tonchev (Houghton)

MSC:

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

Keywords:

Sidon sequence; Sidon set; set of real numbers; differences; bounds