On Rado's Boundedness Conjecture

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:113

Article

Fox, J ; Kleitman, DJ

关键词: rado;    partition regularity;    Rado's Boundedness Conjecture;   

DOI  :  10.1016/j.jcta.2005.07.004

来源: Elsevier

【 摘 要 】

We prove that Rado's Boundedness Conjecture from Richard Rado's 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado's Boundedness Conjecture: if a(1), a(2), and a(3) are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution to the equation a(1)x(1) + a(2)x(2) + a(3)x(3) = 0, then for every finite coloring of the positive integers there is a monochromatic solution to a(1)x(1) + a(2)x(2) + a(3)x(3) = 0. (c) 2005 Elsevier Inc. All rights reserved.

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