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On doubling and volume: chains

Author
Freiman, G.; Serra, O.
Type of activity
Journal article
Journal
Acta Arithmetica
Date of publication
2018-10-01
Volume
186
Number
1
First page
37
Last page
59
DOI
https://doi.org/10.4064/aa170211-8-2 Open in new window
Project funding
Barcelona Graduate School of Mathematics
Discrete, geometric and random structures
Repository
http://hdl.handle.net/2117/125853 Open in new window
URL
https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/186/1/112682/on-doubling-and-volume-chains Open in new window
Abstract
The well-known Freiman–Ruzsa theorem provides a structural description of a set A of integers with |2A|=c|A| as a subset of a d–dimensional arithmetic progression P with |P|=c'|A|, where d and c' depend only on c. The estimation of the constants d and c' involved in the statement has been the object of intense research. Freiman conjectured in 2008 a formula for the largest volume of such a set. In this paper we prove the conjecture for a general class of sets called chains.
Citation
Freiman, G., Serra, O. On doubling and volume: chains. "Acta Arithmetica", 1 Octubre 2018, vol. 186, núm. 1, p. 37-59.
Keywords
Freiman–Ruzsa theorem., additive number theory, sumsets
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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