On long arithmetic progressions in binary Morse-like words
arXiv:2101.02056 · doi:10.1016/j.tcs.2022.08.013
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.
arXiv comment23 pages; comments on binary/non-binary bijective case clarified and result for the binary case stated explicitly in proposition 34
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