Name
Abstract | ||
|---|---|---|
Let gzs(m, 2k) (gzs(m, 2k+1)) be the minimal integer such that for any coloring Δ of the integers from 1, . . . , gzs(m, 2k) by ** (the integers from 1 to gzs(m, 2k+1) by ** ) there exist integers**such that1. there exists jx such that Δ(xi) ∈ ** for each i and ∑i=1m Δ(xi) = 0 mod m (or Δ(xi)=∞ for each i);2. there exists jy such that Δ(yi) ∈ ** for each i and ∑i=1m Δ(yi) = 0 mod m (or Δ(yi)=∞ for each i); and1. 2(xm−x1)≤ym−x1.In this note we show gzs(m, 2)=5m−4 for m≥2, gzs(m, 3)=7m+** −6 for m≥4, gzs(m, 4)=10m−9 for m≥3, and gzs(m, 5)=13m−2 for m≥2. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s00373-005-0636-x | Graphs and Combinatorics |
Keywords | Field | DocType |
Discrete Math, Trivial Fact, Ramsey Number, Positive Integer Solution, Additive Number Theory | Integer,Combinatorics,Ramsey's theorem,Mathematics,Additive number theory | Journal |
Volume | Issue | ISSN |
22 | 3 | 1435-5914 |
Citations | PageRank | References |
2 | 0.42 | 12 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David J. Grynkiewicz | 1 | 42 | 10.33 |
| Andrew Schultz | 2 | 57 | 5.78 |