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Van der Waerden's Theorem and Avoidability in Words
Published 12 Dec 2008 in math.CO and cs.FL | (0812.2466v5)
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.
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