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A multidimensional Rado Theorem
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DOI：10.1016/j.aam.2026.103050.png)
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Abstract
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We extend Deuber's theorem on (m, p, c)-sets to hold over the multidimensional positive integer lattices. This leads to a multidimensional Rado theorem where we are guaranteed monochromatic multidimensional points in all finite colorings of (Z+)d where the ith set of coordinates satisfies the ith given linear Rado system. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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