Name
Abstract | ||
|---|---|---|
We show that for any set $Ssubseteq mathbb{Z}$, $|S|=4$ there exists a 3-coloring of $mathbb{Z}$ 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 $mathbb{Z}^d$, $dgeq 2$. |
Year | Venue | Field |
|---|---|---|
2019 | Integers | Integer,Combinatorics,Mathematics |
DocType | Volume | ISSN |
Journal | 19 | Integers: Electronic Journal of Combinatorial Number Theory 19
(2019) A18 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
7 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Maria Axenovich | 1 | 209 | 33.90 |
| John L. Goldwasser | 2 | 59 | 14.86 |
| Bernard Lidický | 3 | 9 | 5.00 |
| Ryan R. Martin | 4 | 36 | 10.12 |
| David Offner | 5 | 16 | 3.95 |
| John M. Talbot | 6 | 78 | 9.61 |
| Michael Young | 7 | 16 | 4.39 |