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- Title
POLYCHROMATIC COLORINGS ON THE INTEGERS.
- Authors
Axenovich, Maria; Goldwasser, John; Lidický, Bernard; Martin, Ryan R.; Offner, David; Talbot, John; Young, Michael
- Abstract
We show that for any set S ⊆ Z with |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.
- Subjects
INTEGERS; COLORS; LOGICAL prediction; CHROMATIC polynomial
- Publication
Integers: Electronic Journal of Combinatorial Number Theory, 2019, Vol 19, p1
- ISSN
1553-1732
- Publication type
Article