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**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 f_{k}(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 g_{k}(n) be the smallest integer m such that there is a set A \subseteq **{**1,2,...,n-1**}** with m = **sum**_{a in A}a 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 f_{2}(n) \leq [2\sqrt n+ log_{5/4}n+8] and {\sqrt {2n}/8} \leq g_{2}(n)-2n \leq 3 \sqrt n log_{5/4}n, with the lower bound for g_{2}(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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