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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
##### Keywords:
Sidon sequence; Sidon set; set of real numbers; differences; bounds
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