On monochromatic solutions of equations in groups

Peter Cameron*, Javier Cilleruelo, Oriol Serra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We show that the number of monochromatic solutions of the equation x 1 α1x2 α2⋯x r αr = g in a 2-coloring of a finite group G, where α1,...,αr are permutations and g ∈ G, depends only on the cardinalities of the chromatic classes but not on their distribution. We give some applications to arithmetic Ramsey statements.

Original languageEnglish
Pages (from-to)385-395
Number of pages11
JournalRevista Matematica Iberoamericana
Volume23
Issue number1
DOIs
Publication statusPublished - 1 Jan 2007

Keywords

  • Monochromatic arithmetic progressions
  • Orthogonal arrays
  • Schur triples

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