Polychromatic Colorings on the Integers
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2019-01-01
Authors
Axenovich, Maria
Goldwasser, John
Lidicky, Bernard
Martin, Ryan
Offner, David
Talbot, John
Young, Michael
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Lidicky, Bernard
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Mathematics
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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.
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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.
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Tue Jan 01 00:00:00 UTC 2019