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In additive number theory and combinatorics, a restricted sumset has the form where are finite nonempty subsets of a field F and is a polynomial over F. If is a constant non-zero function, for example for any , then S is the usual sumset which is denoted by nA if . When S is written as which is denoted by if . Note that |S| > 0 if and only if there exist with .

Attributes	Values
rdfs:label	Somme restreinte d'ensembles (fr) Restricted sumset (en)
rdfs:comment	In additive number theory and combinatorics, a restricted sumset has the form where are finite nonempty subsets of a field F and is a polynomial over F. If is a constant non-zero function, for example for any , then S is the usual sumset which is denoted by nA if . When S is written as which is denoted by if . Note that \|S\| > 0 if and only if there exist with . (en) En théorie additive des nombres et en combinatoire, une somme restreinte d'ensembles est[réf. souhaitée] un ensemble de la forme où A1, … , An sont des parties d'un groupe abélien G et B est une partie de Gn. Le groupe G considéré est souvent le groupe additif d'un anneau commutatif, comme l'anneau ℤ des entiers ou un anneau ℤ/nℤ. Si l'ensemble B qu'on exclut est vide, S est simplement la somme d'ensembles usuelle A1 + … + An (notée nA si tous les Ak sont égaux à un même ensemble A). Si B est l'ensemble des n-uplets d'éléments non tous distincts, alors S est noté ou encore (fr)
dcterms:subject	Additive number theory Additive combinatorics Sumsets Augustin-Louis Cauchy
Wikipage page ID	7960510 (xsd:integer)
Wikipage revision ID	1054332858 (xsd:integer)
Link from a Wikipage to another Wikipage	Paul Erdős Additive number theory Modular arithmetic Combinatorics Additive number theory Additive combinatorics Total degree Cyclic group Sumsets Field (mathematics) Noga Alon Nullstellensatz Graduate Texts in Mathematics Hans Heilbronn Harold Davenport Augustin-Louis Cauchy Imre Z. Ruzsa Kneser's theorem (combinatorics) Sumset Polynomial method in combinatorics Erdős–Ginzburg–Ziv theorem Springer-Verlag Augustin Louis Cauchy Zhi-Wei Sun
sameAs	Restricted sumset Restricted sumset Restricted sumset Restricted sumset
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Mathworld dbt:Reflist dbt:Short_description
title	Erdős-Heilbronn Conjecture (en)
urlname	Erdos-HeilbronnConjecture (en)
has abstract	En théorie additive des nombres et en combinatoire, une somme restreinte d'ensembles est[réf. souhaitée] un ensemble de la forme où A1, … , An sont des parties d'un groupe abélien G et B est une partie de Gn. Le groupe G considéré est souvent le groupe additif d'un anneau commutatif, comme l'anneau ℤ des entiers ou un anneau ℤ/nℤ. Si l'ensemble B qu'on exclut est vide, S est simplement la somme d'ensembles usuelle A1 + … + An (notée nA si tous les Ak sont égaux à un même ensemble A). Si B est l'ensemble des n-uplets d'éléments non tous distincts, alors S est noté ou encore lorsque tous les Ak sont égaux à A. (fr) In additive number theory and combinatorics, a restricted sumset has the form where are finite nonempty subsets of a field F and is a polynomial over F. If is a constant non-zero function, for example for any , then S is the usual sumset which is denoted by nA if . When S is written as which is denoted by if . Note that \|S\| > 0 if and only if there exist with . (en)
prov:wasDerivedFrom	wikipedia-en:Restricted_sumset?oldid=1054332858&ns=0
page length (characters) of wiki page	7747 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Restricted_sumset
is Link from a Wikipage to another Wikipage of	List of conjectures by Paul Erdős List of number theory topics Combinatorial Nullstellensatz Additive combinatorics Cauchy-Davenport theorem Cauchy–Davenport theorem Erdos-Heilbronn conjecture Erdos–Heilbronn conjecture Erdős-Heilbronn conjecture Erdős–Heilbronn conjecture Barycentric-sum problem Noga Alon Sun Zhiwei List of things named after Augustin-Louis Cauchy Sumset Polynomial method in combinatorics Outline of combinatorics
is Wikipage redirect of	Combinatorial Nullstellensatz Cauchy-Davenport theorem Cauchy–Davenport theorem Erdos-Heilbronn conjecture Erdos–Heilbronn conjecture Erdős-Heilbronn conjecture Erdős–Heilbronn conjecture
is known for of	Noga Alon
is known for of	Noga Alon
is foaf:primaryTopic of	wikipedia-en:Restricted_sumset

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