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On some problems of Euclidean Ramsey theory

O некоторых задачах евклидовой теории Рамсея

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An Erratum to this article was published on 01 September 2016

Abstract

In the paper we prove, in particular, that for any measurable coloring of the euclidean plane with two colours there is a monochromatic triangle with some restrictions on the sides. Also we consider similar problems in finite fields settings.

Резюме

В работе мы, в частности, показываем, что для любой измеримой раскраски евклидовой плоскости в два цвета найдется монохроматический треугольник с некоторыми ограничениями на его стороны. Также мы рассматриваем подобные задачи в пространствах над конечным полем.

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Authors and Affiliations

  1. Steklov Mathematical Institute of RAS, Gubkina str. 8, 119991, Moscow, Russia

    I. D. Shkredov

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  1. I. D. Shkredov
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Correspondence to I. D. Shkredov.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10476-016-0305-8.

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Shkredov, I.D. On some problems of Euclidean Ramsey theory. Anal Math 41, 299–310 (2015). https://doi.org/10.1007/s10476-015-0304-1

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  • DOI: https://doi.org/10.1007/s10476-015-0304-1

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