Van der Waerden's Theorem and Avoidability in Words

Details Van der Waerden's Theorem and Avoidability in Words Van der Waerden's Theorem and Avoidability in Words

2008-12-12

arxiv.org/abs/0812.2466v5

Mathematics

Combinatorics

Co-author added; new results

Scientific paper

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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