The Schur numbers are the numbers in the partitioning of a set which are guaranteed to exist by Schur's Lemma. Schur
numbers satisfy the inequality
See also Ramsey Number, Ramsey's Theorem, Schur's Lemma, Schur's Theorem
References
Frederickson, H. ``Schur Numbers and the Ramsey Numbers
.'' J. Combin. Theory Ser. A
27, 376-377, 1979.
Guy, R. K. ``Schur's Problem. Partitioning Integers into Sum-Free Classes'' and ``The Modular Version of
Schur's Problem.'' §E11 and E12 in
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 209-212, 1994.
Sloane, N. J. A. Sequence
A045652
in ``The On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html.