Published March 30, 2006
| public
Journal Article
Open
Monochromatic and Zero-Sum Sets of Nondecreasing Modified Diameter
- Creators
- Grynkiewicz, David
- Sabar, Rasheed
Abstract
Let m be a positive integer whose smallest prime divisor is denoted by p, and let Zm denote the cyclic group of residues modulo m. For a set B = {x1, x2, ..., xm} of m integers satisfying x1 < x2 < ... < xm, and an integer j satisfying 2 <= j <= m, define gj(B) = xj − x1. Furthermore, define fj(m, 2) (define fj(m, Zm)) to be the least integer N such that for every coloring Delta: {1, ..., N} -> {0, 1} (every coloring Delta : {1, ..., N} -> Zm), there exist two m-sets [see Abstract in the PDF].
Additional Information
Submitted: Oct 24, 2004; Accepted: Mar 24, 2006; Published: Mar 30, 2006 The second author was funded by NSF grant DMS0097317. The authors would like to thank Professor A. Bialostocki for suggesting that we investigate Conjectures 1.1 and 1.2 and for many fruitful discussions. They would also like to thank the referees for their many helpful suggestions.Files
GRYejc06.pdf
Files
(187.8 kB)
Name | Size | Download all |
---|---|---|
md5:ebbf1b4a43e497afd0ffd0e44320f63e
|
187.8 kB | Preview Download |
Additional details
- Eprint ID
- 2656
- Resolver ID
- CaltechAUTHORS:GRYejc06
- Created
-
2006-04-14Created from EPrint's datestamp field
- Updated
-
2019-10-02Created from EPrint's last_modified field