Symmetric sum-free partitions and lower bounds for Schur numbers. (English) Zbl 0944.05093

Fredricksen, Harold; Sweet, Melvin M.

Electron. J. Comb. 7, No. 1, Research paper R32, 9 p. (2000); printed version J. Comb. 7, No. 2 (2000).

Summary: We give new lower bounds for the Schur numbers \(S(6)\) and \(S(7)\). This will imply new lower bounds for the multicolor Ramsey numbers \(R_6(3)\) and \(R_7(3)\). We also make several observations concerning symmetric sum-free partitions into 5 sets.

MSC:

05D10	Ramsey theory
05A18	Partitions of sets

Keywords:

Schur numbers; multicolor Ramsey numbers; symmetric sum-free paritions