This is my first post in this blog. It will be about Euclidean Ramsey theory and possibly about related areas that I am working on. The related areass I am currently working on are the polymath1 project and more specifically the number of points an n-dimensional cube of side three can have without forming a geometric line. This is a spinoff from the main project of finding a combinatorial proof of the density Hales Jewitt theorem for n=3 and generalizing that to higher n.

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This entry was posted on May 2, 2009 at 8:36 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
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May 2, 2009 at 8:36 pm |

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May 26, 2009 at 5:32 pm |

Welcome to WordPress 🙂

June 16, 2009 at 10:54 pm |

Hi Krystal,

I have been wanting to put together a bibliography of papers in Euclidean Ramsey Theory for a while now (at the moment, just for my personal use). I am not a combinatorialist by training, so I may have very easily missed some of the key papers in the area. Are there some that jump to mind?

I have found a few papers by Graham, the 6 author papers by Erdos et al., a paper by Kriz, one by Schmerl, and two by yourself.

June 17, 2009 at 6:35 pm |

I will be looking for more. One that comes to mind is Frankl, P. and Rödl, V., A partition property of simplices in Euclidean space. J. Amer. Math. Soc. 3 No 1, pp. 1–7. This shows that every simplex is Ramsey if I recall correctly.

June 26, 2009 at 1:36 pm

Hi again.

Thanks for the reference!