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Additive and Multiplicative Ramsey Theorems in ℕ – Some Elementary Results†

Published online by Cambridge University Press:  12 September 2008

Vitaly Bergelson  and
Neil Hindman
Vitaly Bergelson
Affiliation:
Department of Mathematics, Ohio State University, Columbus OH 43210, USA
Neil Hindman
Affiliation:
Department of Mathematics, Howard University, Washington DC 20059, USA
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Abstract

We show by elementary methods that given any finite partition of the set ℕ of positive integers, there is one cell that is both additively and multiplicatively rich. In particular, this cell must contain a sequence and all of its finite sums, and another sequence and all of its finite products, a fact that was previously known only by utilizing the algebraic structure of the Stone–Čech compactification βℕ of ℕ.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 3 , September 1993 , pp. 221 - 241
Copyright
Copyright © Cambridge University Press 1993

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