Geodesic
New examples of complete sets, with connections to a Diophantine theorem of Furstenberg
Vitaly Bergelson 1   ; David Simmons 2
1 Department of Mathematics Ohio State University 231 W. 18th Avenue Columbus, OH 43210-1174, U.S.A.
2 Department of Mathematics University of York Heslington, York YO10 5DD, UK
Acta Arithmetica, Tome 177 (2017) no. 2, pp. 101-131 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A set $A\subseteq\mathbb N$ is called complete if every sufficiently large integer can be written as a sum of distinct elements of $A$. We present a new method for proving the completeness of a set, improving results of Cassels (1960), Zannier (1992), Burr, Erdős, Graham, and Li (1996), and Hegyvári (2000). We also introduce the somewhat philosophically related notion of a dispersing set, and refine a theorem of Furstenberg (1967).
DOI : 10.4064/aa8221-10-2016
Keywords: set subseteq mathbb called complete every sufficiently large integer written sum distinct elements nbsp present method proving completeness set improving results cassels zannier burr erd graham hegyv introduce somewhat philosophically related notion dispersing set refine theorem furstenberg

Vitaly Bergelson  1   ; David Simmons  2

1 Department of Mathematics Ohio State University 231 W. 18th Avenue Columbus, OH 43210-1174, U.S.A.
2 Department of Mathematics University of York Heslington, York YO10 5DD, UK 
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     title = {New examples of complete sets, with connections to a {Diophantine} theorem of {Furstenberg}},
     journal = {Acta Arithmetica},
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Vitaly Bergelson; David Simmons. New examples of complete sets, with connections to a Diophantine theorem of Furstenberg. Acta Arithmetica, Tome 177 (2017) no. 2, pp. 101-131. doi: 10.4064/aa8221-10-2016

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