Open Access
April, 2007 On monochromatic solutions of equations in groups
Peter Cameron, Javier Cilleruelo, Oriol Serra
Rev. Mat. Iberoamericana 23(1): 385-395 (April, 2007).


We show that the number of monochromatic solutions of the equation $x_1^{\alpha_1}x_2^{\alpha_2}\cdots x_r^{\alpha_r}=g$ in a $2$-coloring of a finite group $G$, where $\alpha_1,\ldots,\alpha_r$ are permutations and $g\in G$, 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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Peter Cameron. Javier Cilleruelo. Oriol Serra. "On monochromatic solutions of equations in groups." Rev. Mat. Iberoamericana 23 (1) 385 - 395, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1124.05086
MathSciNet: MR2351139

Primary: 05D10

Keywords: monochromatic arithmetic progressions , orthogonal arrays , Schur triples

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 1 • April, 2007
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