On long arithmetic progressions in binary Morse-like words
Combinatorics
2023-04-04 v2 Discrete Mathematics
Dynamical Systems
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.
Cite
@article{arxiv.2101.02056,
title = {On long arithmetic progressions in binary Morse-like words},
author = {Ibai Aedo and Uwe Grimm and Yasushi Nagai and Petra Staynova},
journal= {arXiv preprint arXiv:2101.02056},
year = {2023}
}
Comments
23 pages; comments on binary/non-binary bijective case clarified and result for the binary case stated explicitly in proposition 34