We show that the number of monochromatic solutions of the equation in a -coloring of a finite group , where are permutations and , depends only on the cardinalities of the chromatic classes but not on their distribution. We give some applications to arithmetic Ramsey statements.
Cite this article
Peter J. Cameron, Javier Cilleruelo, Oriol Serra, On monochromatic solutions of equations in groups. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 385–395DOI 10.4171/RMI/499