About: Freiman's theorem

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In additive combinatorics, Freiman's theorem is a central result which indicates the approximate structure of sets whose sumset is small. It roughly states that if is small, then can be contained in a small generalized arithmetic progression.

Attributes	Values
rdf:type	yago:WikicatTheoremsInNumberTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Freiman's theorem (en) Θεώρημα του Φρέιμαν (el) Théorème de Freiman (fr) Teorema de Freiman (pt)
rdfs:comment	Στα μαθηματικά, το Θεώρημα του Φρέιμαν (Freiman) είναι ένα αποτέλεσμα Συνδυαστικής στη Θεωρία των Αριθμών. Κατά μία έννοια συμμετέχει με ποσοστό στην κατά προσέγγιση δομή των συνόλων των ακεραίων, που, λαμβάνοντας δύο την κάθε φορά, περιέχουν υψηλό ποσοστό των εσωτερικών αθροισμάτων τους. (el) In additive combinatorics, Freiman's theorem is a central result which indicates the approximate structure of sets whose sumset is small. It roughly states that if is small, then can be contained in a small generalized arithmetic progression. (en) En mathématiques, le théorème de Freiman est un résultat combinatoire de théorie additive des nombres dû à (en) selon lequel, pour un ensemble fini A d'entiers, si la somme de A avec lui-même n'est « pas trop grosse » par rapport à A, alors A est inclus dans une progression arithmétique généralisée elle-même « pas trop grosse ». (fr) Na matemática, o Teorema de Freiman é um resultado combinatório da teoria dos números. Compreende cálculos da estrutura aproximada de um conjunto de inteiros que contêm uma alta proporção de suas somas internas, tomados dois de cada vez. A demonstração formal é: Tomemos A como um conjunto finito de inteiros em que a soma de conjuntos A + A é pequena, no sentido de que \|A + A\| < c\|A\| para alguma constante c. Existe uma progressão aritmética n-dimensional de grau c′\|A\| que contém A, em que c' e n são funções de c, ou seja, dependem unicamente de c. (pt)
dct:subject	Theorems in number theory Sumsets
Wikipage page ID	2240299 (xsd:integer)
Wikipage revision ID	1040185167 (xsd:integer)
Link from a Wikipage to another Wikipage	Mei-Chu Chang Ben Green (mathematician) Bertrand's postulate Theorems in number theory Generalized arithmetic progression Geometry of numbers Minkowski's theorem Markov spectrum Additive combinatorics Cyclic groups Sumsets Finite field Fourier analysis Terence Tao Solvable groups Codimension Greedy algorithm Gregory Freiman Imre Z. Ruzsa Kneser's theorem (combinatorics) Tom Sanders (mathematician) Sumset Plünnecke-Ruzsa inequality
sameAs	Freiman's theorem Freiman's theorem Freiman's theorem Freiman's theorem Freiman's theorem Freiman's theorem Freiman's theorem Freiman's theorem
dbp:wikiPageUsesTemplate	dbt:Cite_journal dbt:Main dbt:Reflist dbt:Short_description dbt:PlanetMath_attribution
id	4304 (xsd:integer)
title	Freiman's theorem (en)
has abstract	Στα μαθηματικά, το Θεώρημα του Φρέιμαν (Freiman) είναι ένα αποτέλεσμα Συνδυαστικής στη Θεωρία των Αριθμών. Κατά μία έννοια συμμετέχει με ποσοστό στην κατά προσέγγιση δομή των συνόλων των ακεραίων, που, λαμβάνοντας δύο την κάθε φορά, περιέχουν υψηλό ποσοστό των εσωτερικών αθροισμάτων τους. (el) In additive combinatorics, Freiman's theorem is a central result which indicates the approximate structure of sets whose sumset is small. It roughly states that if is small, then can be contained in a small generalized arithmetic progression. (en) En mathématiques, le théorème de Freiman est un résultat combinatoire de théorie additive des nombres dû à (en) selon lequel, pour un ensemble fini A d'entiers, si la somme de A avec lui-même n'est « pas trop grosse » par rapport à A, alors A est inclus dans une progression arithmétique généralisée elle-même « pas trop grosse ». (fr) Na matemática, o Teorema de Freiman é um resultado combinatório da teoria dos números. Compreende cálculos da estrutura aproximada de um conjunto de inteiros que contêm uma alta proporção de suas somas internas, tomados dois de cada vez. A demonstração formal é: Tomemos A como um conjunto finito de inteiros em que a soma de conjuntos A + A é pequena, no sentido de que \|A + A\| < c\|A\| para alguma constante c. Existe uma progressão aritmética n-dimensional de grau c′\|A\| que contém A, em que c' e n são funções de c, ou seja, dependem unicamente de c. (pt)
prov:wasDerivedFrom	wikipedia-en:Freiman's_theorem?oldid=1040185167&ns=0
page length (characters) of wiki page	14395 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Freiman's_theorem
is Link from a Wikipage to another Wikipage of	Mei-Chu Chang Ben Green (mathematician) Generalized arithmetic progression Arithmetic combinatorics Additive combinatorics Nikolay Bogolyubov Freimann Gregory Freiman Imre Z. Ruzsa List of theorems Plünnecke–Ruzsa inequality Sumset Freiman theorem
is Wikipage redirect of	Freiman theorem
is foaf:primaryTopic of	wikipedia-en:Freiman's_theorem

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