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.


5 Responses to “Introduction”

  1. Mr WordPress Says:

    Hi, this is a comment.
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  2. Successful Researcher: How to Become One Says:

    Welcome to WordPress 🙂

  3. andrescaicedo Says:

    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.

    • kristalcantwell Says:

      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.

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