Talbot, J;
Axenovich, M;
Goldwasser, J;
Lidicky, B;
Martin, R;
Offner, D;
Young, M;
(2019)
Polychromatic Colorings on the Integers.
Integers : Electronic Journal of Combinatorial Number Theory
, 19
(A18)
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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.
| Type: | Article |
|---|---|
| Title: | Polychromatic Colorings on the Integers |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://math.colgate.edu/~integers/current.html |
| Language: | English |
| Additional information: | All works of this journal are licensed under a Creative Commons Attribution 4.0 International License so that all content is freely available without charge to the users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This is in accordance with the BOAI definition of open access. http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Ramsey Theory |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10070285 |
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