Euclidean Ramsey Theorems. I
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TLDR
Questions of whether or not certain R are r -Ramsey where B is a Euclidean space and R is defined geometrically are investigated.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-05-01 and is currently open access. It has received 115 citations till now. The article focuses on the topics: Euclidean space.read more
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A hales–jewett type property of finite solvable groups
TL;DR: In this paper, it was shown that Leader, Russell and Walters' conjecture is satisfied in the case of finite solvable groups, which can be used to recover the work of Křiž in Euclidean Ramsey theory.
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All finite configurations are Almost Ramsey
TL;DR: It is shown that under any k -coloration of the points of R N there exists a monochromatic configuration C which may be transformed into a congruent copy of C by moving each point a distance at most ϵ.
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Two-Colorings of Normed Spaces with No Long Monochromatic Unit Arithmetic Progressions
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In Memoriam: Peter L. Montgomery (1947–2020)
Joppe W. Bos,Kristin E. Lauter +1 more
TL;DR: His contributions end up being useful to speed up the arithmetic in virtually all public-key cryptographic systems used around the globe to protect the authors' information today.
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On monochromatic configurations for finite colorings
TL;DR: It is proved that, for any @d >0 and any finite coloring of the plane, there exist infinitely many monochromatic trapezoids of area @d>0 that are translates of the same trapezoid.
References
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On a Problem of Formal Logic
TL;DR: This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula.
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Regularity and Positional Games
A. W. Hales,R. I. Jewett +1 more
TL;DR: In this paper, it was shown that a set is n-regular in X if, for any partition of X into N parts, some part has as a subset a member of the set.