Frankl, Peter; Graham, Ronald L.; Rödl, Vojtěch Quantitative versions of combinatorial partition theorems. (Quantitative Versionen von kombinatorischen Partitionssätzen.) (German) Zbl 0737.05012 Jahresber. Dtsch. Math.-Ver. 92, No. 3, 130-144 (1990). There are many “Ramsey theorems”, the most famous of which are Schur’s theorem (see Über die Kongruenz \(x^ m+y^ m\equiv z^ m(\mod p)\), Jahresber. Dtsch. Math.-Ver. 25, 114-116 (1916)), van der Waerden’s theorem (see B. L. van der Waerden, Beweis einer Baudetschen Vermutung, Nieuw Arch. Wisk. 15, 212-216 (1927)), and Ramsey’s theorem (see F. P. Ramsey, On a problem in formal logic, Proc. London Math. Soc. (2) 30, 264-285 (1930)). These theorems all all deal with partitions of the infinite set of natural numbers. In the present paper the authors are concerned with theorems of a similar kind, except that they now deal with partitions of a finite set of natural numbers \(\{1,2,\ldots,N\}\). Reviewer: E.J.F.Primrose (Leicester) MSC: 05A17 Combinatorial aspects of partitions of integers 05C55 Generalized Ramsey theory 11P81 Elementary theory of partitions Keywords:partition theorems PDF BibTeX XML Cite \textit{P. Frankl} et al., Jahresber. Dtsch. Math.-Ver. 92, No. 3, 130--144 (1990; Zbl 0737.05012) OpenURL