More on lines in Euclidean Ramsey theory
Let $\ell _m$ be a sequence of $m$ points on a line with consecutive points at distance one. Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number $m$ and a red/blue-colouring of $\mathbb{E}^n$ for every $n$ that cont...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.452/ |
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| author | Conlon, David Wu, Yu-Han |
| author_facet | Conlon, David Wu, Yu-Han |
| author_sort | Conlon, David |
| collection | DOAJ |
| description | Let $\ell _m$ be a sequence of $m$ points on a line with consecutive points at distance one. Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number $m$ and a red/blue-colouring of $\mathbb{E}^n$ for every $n$ that contains no red copy of $\ell _3$ and no blue copy of $\ell _m$. |
| format | Article |
| id | doaj-art-f58670afdb9940acb8743733dd639288 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-f58670afdb9940acb8743733dd6392882025-02-07T11:08:08ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-07-01361G589790110.5802/crmath.45210.5802/crmath.452More on lines in Euclidean Ramsey theoryConlon, David0Wu, Yu-Han1Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USAÉcole Normale Supérieure - PSL, Paris, FranceLet $\ell _m$ be a sequence of $m$ points on a line with consecutive points at distance one. Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number $m$ and a red/blue-colouring of $\mathbb{E}^n$ for every $n$ that contains no red copy of $\ell _3$ and no blue copy of $\ell _m$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.452/ |
| spellingShingle | Conlon, David Wu, Yu-Han More on lines in Euclidean Ramsey theory Comptes Rendus. Mathématique |
| title | More on lines in Euclidean Ramsey theory |
| title_full | More on lines in Euclidean Ramsey theory |
| title_fullStr | More on lines in Euclidean Ramsey theory |
| title_full_unstemmed | More on lines in Euclidean Ramsey theory |
| title_short | More on lines in Euclidean Ramsey theory |
| title_sort | more on lines in euclidean ramsey theory |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.452/ |
| work_keys_str_mv | AT conlondavid moreonlinesineuclideanramseytheory AT wuyuhan moreonlinesineuclideanramseytheory |