Name
Abstract | ||
|---|---|---|
Let A be a finite set of integers. We say that A tiles the integers if there is a set T ⊆ ℤ such that {t+A: t∈T{ forms a disjoint partition of the integers. It has long been known that such a set T must be periodic. The question is to determine how long the period of T can become as a function of the diameter of the set A. The previous best lower bound, due to Kolountzakis [7], shows that the period of T can grow as fast as the square of the diameter of A. In this paper we improve Kolountzakis’ lower bound by showing that the period of T can in fact grow faster than any power of the diameter of A. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s00493-009-2269-9 | Combinatorica |
Keywords | Field | DocType |
superpolynomial period,finite set,disjoint partition,lower bound | Integer,Discrete mathematics,Combinatorics,Finite set,Disjoint sets,Upper and lower bounds,Partition (number theory),Periodic graph (geometry),Mathematics | Journal |
Volume | Issue | ISSN |
29 | 4 | 0209-9683 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| John P. Steinberger | 1 | 329 | 18.30 |