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ADDITIVE DIMENSION AND A THEOREM OF SANDERS

Part of: Sequences and sets

Published online by Cambridge University Press:  22 October 2015

TOMASZ SCHOEN  and
ILYA D. SHKREDOV
TOMASZ SCHOEN
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland email schoen@amu.edu.pl
ILYA D. SHKREDOV*
Affiliation:
Division of Algebra and Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow, 119991, Russia Delone Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Sovetskaya str. 14, Yaroslavl, 150000, Russia IITP RAS, Bolshoy Karetny per. 19, Moscow, 127994, Russia email ilya.shkredov@gmail.com
*
✉ilya.shkredov@gmail.com
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Abstract

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We prove some new bounds for the size of the maximal dissociated subset of structured (having small sumset, large energy and so on) subsets of an abelian group.

Keywords

additive dimensionsumsetadditive energydissociated sets

MSC classification

Primary: 11B13: Additive bases, including sumsets
Secondary: 11B75: Other combinatorial number theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 1 , February 2016 , pp. 124 - 144
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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