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On Regressive Ramsey Numbers
by
Peter Blanchard
Denison University, Granville, Ohio
A function f:[X]n --> N is regressive if f(s) < min(s) for all s in [X]n such that min(s) > 0, where X subset or equal N is a set of natural numbers. A set H subset or equal X is min-homogeneous for f if f(s) depends only on min(s) for all s in [H]n. The regressive Ramsey number Rnreg(k) is the least m so that any regressive coloring of [m]n must have a min-homogeneous set of order k.
In this talk we announce several regressive Ramsey numbers, discuss bounds for some regressive Ramsey numbers, and describe a relation between regressive Ramsey numbers and ordinary Ramsey numbers.
Date received: April 12, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cags-21.