Korean J. Math.  Vol 28, No 2 (2020)  pp.379-389
DOI: https://doi.org/10.11568/kjm.2020.28.2.379

$2$-color Rado number for $x_1 +x_2 +\cdots +x_n=y_1 +y_2=z$

Byeong Moon Kim, Woonjae Hwang, Byung Chul Song

Abstract


An $r$-color Rado number $N=R(\mathcal{L},r)$  for a system $\mathcal{L}$ of equations is the least integer, provided it exists, such that for every $r$-coloring of the set $\{1,2, \dots, N\}$, there is a monochromatic solution to $\mathcal{L}$. In this paper, we study the $2$-color  Rado number $R(\mathcal{E},2)$ for $\mathcal{E}: x_1 +x_2 +\cdots +x_n=y_1 +y_2=z$ when $n\ge 4$.


Keywords


Rado number; Schur number; Ramsey theory; r-coloring

Subject classification

05D10;05C55

Sponsor(s)

Basic Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education

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