Quantitative versions of combinatorial partition theorems. (Quantitative Versionen von kombinatorischen Partitionssätzen.) (German) Zbl 0737.05012

Frankl, Peter; Graham, Ronald L.; Rödl, Vojtěch

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