On long arithmetic progressions in binary Morse-like words

01/06/2021

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by   Ibai Aedo, et al.

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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.