Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915024706994176 |
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| author | Currier, Gabriel Moore, Kenneth Yip, Chi Hoi |
| author_facet | Currier, Gabriel Moore, Kenneth Yip, Chi Hoi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions Currier, Gabriel Moore, Kenneth Yip, Chi Hoi Combinatorics 05D10, 52C10 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. |
| title | Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions |
| topic | Combinatorics 05D10, 52C10 |
| url | https://arxiv.org/abs/2402.14197 |