Monochromatic sums and products in

Joel Moreira*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

An old question in Ramsey theory asks whether any finite coloring of the natural numbers admits a monochromatic pair fx+y; xyg. We answer this question affirmatively in a strong sense by exhibiting a large new class of nonlinear patterns that can be found in a single cell of any finite partition of N. Our proof involves a correspondence principle that transfers the problem into the language of topological dynamics. As a corollary of our main theorem we obtain partition regularity for new types of equations, such as x2 - y2 = z and x2 + 2y2 - 3z2 = w.

Original languageEnglish (US)
Pages (from-to)1069-1090
Number of pages22
JournalAnnals of Mathematics
Volume185
Issue number3
DOIs
StatePublished - Jan 1 2017

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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