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Freiman's theorem

In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose sumset is small. It roughly states that if | A + A | / | A | {\displaystyle |A+A|/|A|} is small, then A {\displaystyle A} can be contained in a small generalized arithmetic progression.

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History of Freiman's theorem

Gregory FreimanImre Z. RuzsaMei-Chu ChangTom Sanders
4 related topics

Tools used in the proof

Abelian groupGreedy algorithmCyclic groupsFinite fieldCodimension
8 related topics

Generalizations

Ben GreenTerry TaoSolvable groupsKneserKatalin Marton
7 related topics

Proof

Bertrand's postulate
1 related topics

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Overview

History of Freiman's theorem

Tools used in the proof

Proof

Generalizations

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Freiman's theorem

Nodes29
Edges28
Triples26
Avg. degree1.93
Density0.068966
Components1

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Freiman's theorem

Top relations

related to Bohr sets and Bogolyubov's lemma · 9
Freiman's theorem → Bogolyubov, Bohr, Generalizing, Let, Ruzsa, So, The, The Bohr, Though Freiman's
related to Further reading · 8
Freiman's theorem → Astérisque, Creative Commons Attribution/Share-Alike License, Freiman, Freiman's, PlanetMath, Structure, This, Zbl
related to Generalizations · 8
Freiman's theorem → Ben Green, CK, Freiman's, Green, Imre Ruzsa, Ruzsa, The, They
is a · 1
Freiman's theorem → central result which indicates the approximate structure of sets whose sumset is small

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Important terminology

displaystyle freiman ruzsa theorem generalized arithmetic proof lemma progression mathbb leq freiman's set subseteq subset dimension -isomorphism sets following cdot

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Freiman's theoremis acentral result which indicates the approximate structure of sets whose sumset is small0.90text
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaThough Freiman's0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaRuzsa0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaSo0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaThe0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaBogolyubov0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaGeneralizing0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaBohr0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaLet0.60section
Freiman's theoremrelated to Bohr sets and Bogolyubov's lemmaThe Bohr0.60section
Freiman's theoremrelated to Further readingFreiman0.60section
Freiman's theoremrelated to Further readingStructure0.60section

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