Polychromatic Euclidean Ramsey theoréms
✍ Scribed by P. Erdös; B. Rothschild; E. G. Straus
- Book ID
- 112651586
- Publisher
- Springer
- Year
- 1983
- Tongue
- English
- Weight
- 299 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0047-2468
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract Let us call a finite subset __X__ of a Euclidean __m__‐space E^m^ __Ramsey__ if for any positive integer __r__ there is an integer __n__ = __n__(__X;r__) such that in any partition of E^n^ into __r__ classes __C__~1~,…, __C~r~__, some __C~i~__ contains a set __X__' which is the image of
In this note we shall prove a geometric Ramsey theorem. Let T be a triangle with angles 30, 60 and 90 degrees, and with hypotenus of unit length. Then the theorem says that if one threecolors the 3-space, then there is always a copy of T with monochromatic vertices. We shall also show that there is