𝔖 Bobbio Scriptorium
✦   LIBER   ✦

OLD AND NEW EUCLIDEAN RAMSEY THEOREMS

✍ Scribed by R. L. Graham

Book ID
118722205
Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
413 KB
Volume
440
Category
Article
ISSN
0890-6564

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πŸ“œ SIMILAR VOLUMES

A Euclidean Ramsey theorem
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✍ M. BΓ³na πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 168 KB

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

Euclidean Ramsey theorems on the n-spher
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✍ H. L. Graham πŸ“‚ Article πŸ“… 1983 πŸ› John Wiley and Sons 🌐 English βš– 340 KB πŸ‘ 1 views

## 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