Name
Abstract | ||
|---|---|---|
The 2-color Rado number for the equation x1+x2−2x3=c, which for each constant c∈Z we denote by S1(c), is the least integer, if it exists, such that every 2-coloring, Δ:[1,S1(c)]→{0,1}, of the natural numbers admits a monochromatic solution to x1+x2−2x3=c, and otherwise S1(c)=∞. We determine the 2-color Rado number for the equation x1+x2−2x3=c, when additional inequality restraints on the variables are added. In particular, the case where we require x2<x3<x1, is a generalization of the 3-term arithmetic progression; and the work done here improves previously established upper bounds to an exact value. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1016/j.disc.2003.06.007 | Discrete Mathematics |
Keywords | Field | DocType |
05D10 | Integer,Discrete mathematics,Natural number,Combinatorics,Upper and lower bounds,Rado graph,Mathematics,Arithmetic progression | Journal |
Volume | Issue | ISSN |
280 | 1 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David J. Grynkiewicz | 1 | 42 | 10.33 |