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arXiv · 2402.14197

Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions

Gabriel Currier·Kenneth Moore·Chi Hoi Yip
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Abstract

A conjecture of Erdős, Graham, Montgomery, Rothschild, Spencer and Straus states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monochromatic congruent copy of every three-point configuration. This conjecture is known only for special classes of configurations. In this manuscript, we confirm one of the most natural open cases; that is, every two-coloring of the plane admits a monochromatic congruent copy of any $3$-term arithmetic progression.

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Gabriel Currier, Kenneth Moore, Chi Hoi Yip. 2024-07-22. Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions. https://doi.org/10.1007/s00493-024-00122-2

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