Any Two-Coloring of the Plane Contains Monochromatic 3-Term Arithmetic Progressions

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2024-11-07 DOI:10.1007/s00493-024-00122-2

Gabriel Currier, Kenneth Moore, Chi Hoi Yip

引用次数: 0

Abstract

A conjecture of Erdős, Graham, Montgomery, Rothschild, Spencer, and Straus states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monochromatic congruent copy of every three-point configuration. This conjecture is known only for special classes of configurations. In this manuscript, we confirm one of the most natural open cases; that is, every two-coloring of the plane admits a monochromatic congruent copy of any 3-term arithmetic progression.

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平面的任意双色包含单色三项算术级数

厄尔多斯、格雷厄姆、蒙哥马利、罗斯柴尔德、斯宾塞和斯特劳斯的一个猜想指出，除等边三角形外，平面的任何二色都会有一个三点构型的单色全等副本。这一猜想只适用于特殊类别的构型。在本手稿中，我们证实了其中一种最自然的开放情况，即平面的任何二色配置都有任何三项算术级数的单色全等副本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.