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Title:
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On doubling and volume: chains
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Author:
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Freiman, Gregory A.; Serra Albó, Oriol
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
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Abstract:
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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. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
-Sequences (Mathematics)
-Partitions (Mathematics)
-additive number theory
-sumsets
-Freiman–Ruzsa theorem.
-Successions (Matemàtica)
-Particions (Matemàtica)
-Classificació AMS::11 Number theory::11B Sequences and sets
-Classificació AMS::11 Number theory::11P Additive number theory; partitions |
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Rights:
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Document type:
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Article - Submitted version
Article |
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Published by:
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\Institute of Mathematics, Polish Academy of Sciences\
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