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:
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arXiv e-prints
- Pub Date:
- December 2008
- DOI:
- 10.48550/arXiv.0812.2466
- arXiv:
- arXiv:0812.2466
- Bibcode:
- 2008arXiv0812.2466A
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Formal Languages and Automata Theory;
- 68R15;
- 20M35;
- 68Q45;
- 11B25;
- 10A50
- E-Print:
- Co-author added