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New examples of complete sets, with connections to a Diophantine theorem of Furstenberg

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Publication details

JournalActa Arithmetica
DateAccepted/In press - 16 Sep 2016
DateE-pub ahead of print (current) - 28 Dec 2016
Issue number2
Volume177
Number of pages31
Pages (from-to)101-131
Early online date28/12/16
Original languageEnglish

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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© 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.

    Research areas

  • math.CO

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