Bergelson, Vitaly and Simmons, David orcid.org/0000-0002-9136-6635 (2016) New examples of complete sets, with connections to a Diophantine theorem of Furstenberg. Acta Arithmetica. pp. 101-131. ISSN 1730-6264
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).
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Item Type: | Article | ||||
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Copyright, Publisher and Additional Information: | © 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 | ||||
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Institution: | The University of York | ||||
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) | ||||
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Depositing User: | Pure (York) | ||||
Date Deposited: | 21 Feb 2017 12:00 | ||||
Last Modified: | 25 Mar 2024 00:08 | ||||
Published Version: | https://doi.org/10.4064/aa8221-10-2016 | ||||
Status: | Published online | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.4064/aa8221-10-2016 | ||||
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