Monochromatic solutions to systems of exponential equations

摘要

Let n is an element of N, R be a binary relation on [n], and C-1(i, j), . . . , C-n(i, j) is an element of Z, for i, j is an element of [n]. We define the exponential system of equations epsilon(R, (C-k(i, j)(i,) (j,) (k)) to be the system