Campus Units
Mathematics
Document Type
Article
Publication Version
Published Version
Publication Date
2019
Journal or Book Title
Integers
Volume
19
First Page
A18
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.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Owner
The Authors
Copyright Date
2019
Language
en
File Format
application/pdf
Recommended Citation
Axenovich, Maria; Goldwasser, John; Lidicky, Bernard; Martin, Ryan R.; Offner, David; Talbot, John; and Young, Michael, "Polychromatic Colorings on the Integers" (2019). Mathematics Publications. 178.
https://lib.dr.iastate.edu/math_pubs/178
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.