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- W2950864745 abstract "A linear equation is $r$-regular, if, for every $r$-coloring of the positive integers, there exist positive integers of the same color which satisfy the equation. In 2005, Fox and Radoicic conjectured that the equation $x_1 + 2x_2 + cdots + 2^{n-2}x_{n-1} - 2^{n-1}x_n = 0$, for any $n geq 2$, has a degree of regularity of $n-1$, which would verify a conjecture of Rado from 1933. Rado's conjecture has since been verified with a different family of equations. In this paper, we show that Fox and Radoicic's family of equations indeed have a degree of regularity of $n-1$. We also provide a few extensions of this result." @default.
- W2950864745 created "2019-06-27" @default.
- W2950864745 creator A5089252105 @default.
- W2950864745 date "2014-04-13" @default.
- W2950864745 modified "2023-09-27" @default.
- W2950864745 title "Resolving a Conjecture on Degree of Regularity of Linear Homogeneous Equations" @default.
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