Van der Waerden's Theorem and Avoidability in Words

2008/12/12 by Yu-Hin Au, Aaron Robertson, Au, Yu-Hin +3 · 1 citation
Computer Science · Mathematics · #10A50 #11B25 #20M35 #68Q45 #68R15 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #cs.FL #math.CO #msc:10A50 #msc:11B25 #msc:20M35 #msc:68Q45 #msc:68R15

paper · pdf · doi:10.48550/arxiv.0812.2466

Co-author added; new results

arxiv created 2009/11/17 · arxiv updated 2009/12/01

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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