On long arithmetic progressions in binary Morse-like words

Published 6 Jan 2021 in math.CO, cs.DM, and math.DS | (2101.02056v2)

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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