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On Sumsets of Convex Sets

Published online by Cambridge University Press:  07 July 2011

TOMASZ SCHOEN  and
ILYA D. SHKREDOV
TOMASZ SCHOEN
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland (e-mail: schoen@amu.edu.pl)
ILYA D. SHKREDOV
Affiliation:
Division of Algebra and Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow, 119991Russia (e-mail: ilya.shkredov@gmail.com)
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Abstract

A set of reals A = {a1,. . .,an} is called convex if ai+1 − ai > ai − ai−1 for all i. We prove, among other results, that for some c > 0 every convex A satisfies |A−A| ≥ c|A|8/5log−2/5|A|.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 5 , September 2011 , pp. 793 - 798
Copyright
Copyright © Cambridge University Press 2011

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