On monochromatic solutions of equations in groups

Peter Cameron; Javier Cilleruelo; Oriol Serra

doi:10.4171/RMI/499

On monochromatic solutions of equations in groups

Peter Cameron^*, Javier Cilleruelo, Oriol Serra

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

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,...,α_r 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 language	English
Pages (from-to)	385-395
Number of pages	11
Journal	Revista Matematica Iberoamericana
Volume	23
Issue number	1
DOIs	https://doi.org/10.4171/RMI/499
Publication status	Published - 1 Jan 2007

Keywords

Monochromatic arithmetic progressions
Orthogonal arrays
Schur triples

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10.4171/RMI/499

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AB - 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.

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KW - Schur triples

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On monochromatic solutions of equations in groups

Abstract

Keywords

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