CaltechAUTHORS
  A Caltech Library Service

Monochromatic and Zero-Sum Sets of Nondecreasing Modified Diameter

Grynkiewicz, David and Sabar, Rasheed (2006) Monochromatic and Zero-Sum Sets of Nondecreasing Modified Diameter. Electronic Journal of Combinatorics, 13 (R28). ISSN 1077-8926. https://resolver.caltech.edu/CaltechAUTHORS:GRYejc06

[img]
Preview
PDF
See Usage Policy.

183Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:GRYejc06

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].


Item Type:Article
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.
Issue or Number:R28
Record Number:CaltechAUTHORS:GRYejc06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:GRYejc06
Alternative URL:http://www.combinatorics.org/Volume_13/Abstracts/v13i1r28.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2656
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:14 Apr 2006
Last Modified:02 Oct 2019 22:55

Repository Staff Only: item control page