Van der Waerden's Theorem and Avoidability in Words.

Independently, Pirillo and Varricchio, Halbeisen and Hungerbüühler and Freedman considered the following problem, open since 1992: Does there exist an infinite word w over a finite subset of ℤℤ such that w contains no two consecutive blocks of the same length and sum? We consider some variations on this problem in the light of van der Waerden's theorem on arithmetic progressions. [ABSTRACT FROM AUTHOR]