| Title | On the Dimension of Iterated Sumsets |
| Authors | Jörg Schmeling, Pablo Shmerkin |
| Alternative Location | http://dx.doi.org/10.1007/9..., Restricted Access |
| Publication | Recent Developments in Fractals and Related Fields |
| Year | 2010 |
| Pages | 55 - 72 |
| Document type | Conference paper |
| Conference name | Conference on Fractals and Related Fields |
| Conference Date | Sep, 2007 |
| Conference Location | Monastir, Tunisia |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Birkhäuser Boston |
| Abstract English | Let A be a subset of the real line. We study the fractal dimensions of the k-fold iterated sumsets kA, defined as kA = {a(1) ... + a(k) : a(i) is an element of A}. We show that for any nondecreasing sequence {alpha(k)}(k=1)(infinity) taking values in 0,1, there exists a compact set A such that kA has Hausdorff dimension ak for all k >= 1. We also show how to control various kinds of dimensions simultaneously for families of iterated sumsets. These results are in stark contrast to the Plunnecke-Ruzsa inequalities in additive combinatorics. However, for lower box-counting dimensions, the analog of the Pliinnecke Ruzsa inequalities does hold. |
| ISBN/ISSN/Other | ISBN: 978-0-8176-4887-9 |
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