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Van der Waerden's Theorem and Avoidability in Words

Authors
  • Au, Yu-Hin
  • Robertson, Aaron
  • Shallit, Jeffrey
Type
Preprint
Publication Date
Nov 17, 2009
Submission Date
Dec 12, 2008
Source
arXiv
License
Yellow
External links

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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