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JCT
2006

On Rado's Boundedness Conjecture

13 years 5 months ago
On Rado's Boundedness Conjecture
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 a1, a2, and a3 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 a1x1 + a2x2 + a3x3 = 0, then for every finite coloring of the positive integers there is a monochromatic solution to a1x1 + a2x2 + a3x3 = 0. Key words: Rado, Partition Regularity, Rado's Boundedness Conjecture
Jacob Fox, Daniel J. Kleitman
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JCT
Authors Jacob Fox, Daniel J. Kleitman
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