On monochromatic solutions of equations in groups
Cameron, Peter ; Cilleruelo, Javier ; Serra, Oriol
Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, p. 385-395 / Harvested from Project Euclid
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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.
Publié le : 2007-04-14
Classification:  orthogonal arrays,  Schur triples,  monochromatic arithmetic progressions,  05D10 
@article{1180728898,
     author = {Cameron, Peter and Cilleruelo, Javier and Serra, Oriol},
     title = {On monochromatic solutions of equations in groups},
     journal = {Rev. Mat. Iberoamericana},
     volume = {23},
     number = {1},
     year = {2007},
     pages = { 385-395},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1180728898}
}

Cameron, Peter; Cilleruelo, Javier; Serra, Oriol. On monochromatic solutions of equations in groups. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp.  385-395. http://gdmltest.u-ga.fr/item/1180728898/