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Polychromatic Colorings on the Integers
Integers
  • Maria Axenovich, Karlsruhe Institute of Technology
  • John Goldwasser, West Virginia University
  • Bernard Lidicky, Iowa State University
  • Ryan R. Martin, Iowa State University
  • David Offner, Westminster College
  • John Talbot, University College London
  • Michael Young, Iowa State University
Document Type
Article
Publication Version
Published Version
Publication Date
1-1-2019
Abstract

We show that for any set S ⊆ Z, |S| = 4 there exists a 3-coloring of Z in which every translate of S receives all three colors. This implies that S has a codensity of at most 1/3, proving a conjecture of Newman. We also consider related questions in Zd, d ≥ 2.

Comments

This article is published as M. Axenovich, J. Goldwasser, B. Lidický, R. Martin, D. Offner, J. Talbot, M. Young. Polychromatic Colorings on the Integers. Integers 19 (2019): A18.

Creative Commons License
Creative Commons Attribution 4.0
Copyright Owner
The Authors
Language
en
File Format
application/pdf
Citation Information
Maria Axenovich, John Goldwasser, Bernard Lidicky, Ryan R. Martin, et al.. "Polychromatic Colorings on the Integers" Integers Vol. 19 (2019) p. A18
Available at: http://0-works.bepress.com.library.simmons.edu/bernard-lidicky/48/