Van der Waerden's Theorem and Avoidability in Words
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.
 Publication:

arXiv eprints
 Pub Date:
 December 2008
 arXiv:
 arXiv:0812.2466
 Bibcode:
 2008arXiv0812.2466A
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Formal Languages and Automata Theory;
 68R15;
 20M35;
 68Q45;
 11B25;
 10A50
 EPrint:
 Coauthor added