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.

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 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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