Name
Abstract | ||
|---|---|---|
M. Beiglbock, V. Bergelson, and A. Fish proved that if G is a countable amenable group and A and B are subsets of G with positive Banach density, then the product set AB is piecewise syndetic. This means that there is a finite subset E of G such that EAB is thick, that is, EAB contains translates of any finite subset of G. When G = Z, this was first proven by R. Jin. We prove a quantitative version of the aforementioned result by providing a lower bound on the density (with respect to a Folner sequence) of the set of witnesses to the thickness of EAB. When G = Z(d), this result was first proven by the current set of authors using completely different techniques. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1017/jsl.2015.75 | JOURNAL OF SYMBOLIC LOGIC |
Keywords | Field | DocType |
amenable groups,piecewise syndeticity,product sets | Discrete mathematics,Amenable group,Countable set,Cartesian product,Upper and lower bounds,High density,Følner sequence,Piecewise,Mathematics | Journal |
Volume | Issue | ISSN |
81 | 4 | 0022-4812 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mauro Di Nasso | 1 | 7 | 4.36 |
| Isaac Goldbring | 2 | 6 | 5.30 |
| renling jin | 3 | 33 | 10.72 |
| Steven C. Leth | 4 | 23 | 6.02 |
| Martino Lupini | 5 | 0 | 0.34 |
| Karl Mahlburg | 6 | 13 | 5.84 |