## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  789.11007
Autor:  Bollobás, Béla; Erdös, Paul; Jin, Guoping
Title:  Ramsey problems in additive number theory. (In English)
Source:  Acta Arith. 64, No.4, 341-355 (1993).
Review:  Let fk(n) be the minimal integer m such that, for any decomposition of the set {1,...,m} into k (disjoint) classes, n is the sum of distinct terms of one of them. Similarly, let gk(n) be the smallest integer m such that there is a set A \subseteq {1,2,...,n-1} with m = suma in Aa such that, for any partition of A into k classes, n is always the sum of elements of one of them. The authors prove that for all suffciently large n,

[2\sqrt n]+2 \leq f2(n) \leq [2\sqrt n+ log5/4n+8]

and {\sqrt {2n}/8} \leq g2(n)-2n \leq 3 \sqrt n log5/4n, with the lower bound for g2(n) holding even for all n \geq 3.
Reviewer:  B.Volkmann (Stuttgart)
Classif.:  * 11B13 Additive bases
05D05 Extremal set theory
Keywords:  sum-sets; additive representations; Ramsey problems

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