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Element-Distinct Solution For Rado's Theorem

Published 26 Nov 2024 in math.CO | (2411.17456v2)

Abstract: In this paper, we present a simplified proof of Rado's Theorem and demonstrate that when an integer matrix $M$ satisfies the column condition and $M\mathbf x=\mathbf 0$ has an element-distinct solution on $\mathbb N$, then under any finite coloring of $\mathbb N$, the equation $M\mathbf x=\mathbf 0$ has a monochromatic element-distinct solution. This gives a positive answer to a problem of Di Nasso in 2016.

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Authors (2)

  1. Ningyuan Yang 
  2. Tianyi Tao 

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