Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Yang, Ningyuan, Tao, Tianyi
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405029232