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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.

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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].

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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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2656
Deposited By: Archive Administrator
Deposited On:14 Apr 2006
Last Modified:02 Oct 2019 22:55

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