Determination of the two-color Rado number for $a_1x_1+...+a_mx_m=x_0$
| dc.creator | Guo, Song | |
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2006-01-17 | |
| dc.date | 2007-12-24 | |
| dc.date.accessioned | 2026-07-07T08:50:57Z | |
| dc.date.available | 2026-07-07T08:50:57Z | |
| dc.description | For positive integers $a_1,a_2,...,a_m$, we determine the least positive integer $R(a_1,...,a_m)$ such that for every 2-coloring of the set $[1,n]={1,...,n}$ with $n\ge R(a_1,...,a_m)$ there exists a monochromatic solution to the equation $a_1x_1+...+a_mx_m=x_0$ with $x_0,...,x_m\in[1,n]$. The precise value of $R(a_1,...,a_m)$ is shown to be $av^2+v-a$, where $a=min{a_1,...,a_m}$ and $v=\sum_{i=1}^{m}a_i$. This confirms a conjecture of B. Hopkins and D. Schaal. | |
| dc.identifier | https://arxiv.org/abs/math/0601409 | |
| dc.identifier | http://arxiv.org/abs/math/0601409 | |
| dc.identifier | J. Combin. Theory Ser. A 115(2008), 345-353 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144774 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05D10; 11B75; 11D04 | |
| dc.title | Determination of the two-color Rado number for $a_1x_1+...+a_mx_m=x_0$ | |
| dc.type | text |