Projects per year
Abstract
A set $A\subseteq\mathbb N$ is called $complete$ if every sufficiently large integer can be written as the sum of distinct elements of $A$. In this paper we present a new method for proving the completeness of a set, improving results of Cassels ('60), Zannier ('92), Burr, Erd\H{o}s, Graham, and Li ('96), and Hegyv\'ari ('00). We also introduce the somewhat philosophically related notion of a $dispersing$ set and refine a theorem of Furstenberg ('67).
Original language | English |
---|---|
Pages (from-to) | 101-131 |
Number of pages | 31 |
Journal | Acta Arithmetica |
Volume | 177 |
Issue number | 2 |
Early online date | 28 Dec 2016 |
DOIs | |
Publication status | E-pub ahead of print - 28 Dec 2016 |
Bibliographical note
© Instytut Matematyczny PAN, 2017.This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.Keywords
- math.CO
Projects
- 1 Finished
-
Programme Grant-New Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research