Van der Waerden's Theorem and Avoidability in Words

  title={Van der Waerden's Theorem and Avoidability in Words},
  author={Yu Hin Au and Aaron Robertson and Jeffrey Shallit},
Abstract Independently, Pirillo and Varricchio, Halbeisen and Hungerbühler and Freedman considered the following problem, open since 1992: 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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