2000 character limit reached
Van der Waerden's Theorem and Avoidability in Words (0812.2466v5)
Published 12 Dec 2008 in math.CO and cs.FL
Abstract: Pirillo and Varricchio, and independently, Halbeisen and Hungerbuhler considered the following problem, open since 1994: Does there exist an infinite word w over a finite subset of Z 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.