Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

8-3-2018

Journal or Book Title

arxiv

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 [D. J. Newman, Complements of finite sets of integers, Michigan Math. J. 14 (1967) 481–486]. We also consider related questions in Zd, d ≥ 2.

Comments

This is a manuscript made available through arxiv: https://arxiv.org/abs/1704.00042.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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