Van der Waerden's Theorem and Avoidability in Words
Combinatorics
2009-11-17 v5 Formal Languages and Automata Theory
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.
Cite
@article{arxiv.0812.2466,
title = {Van der Waerden's Theorem and Avoidability in Words},
author = {Yu-Hin Au and Aaron Robertson and Jeffrey Shallit},
journal= {arXiv preprint arXiv:0812.2466},
year = {2009}
}
Comments
Co-author added; new results