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arXiv · 2101.02056

On long arithmetic progressions in binary Morse-like words

Ibai Aedo·Uwe Grimm·Yasushi Nagai·Petra Staynova
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Abstract

We present results on the existence of long arithmetic progressions in the Thue-Morse word and in a class of generalised Thue-Morse words. Our arguments are inspired by van der Waerden's proof for the existence of arbitrary long monochromatic arithmetic progressions in any finite colouring of the (positive) integers.

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Ibai Aedo, Uwe Grimm, Yasushi Nagai, Petra Staynova. 2021-02-09. On long arithmetic progressions in binary Morse-like words. https://doi.org/10.1016/j.tcs.2022.08.013

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