Kneser's theorem (combinatorics): Difference between revisions

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In mathematics, '''Kneser's theorem''' is an [[Inequality (mathematics)|inequality]] among the sizes of certain [[sumset]]s in [[abelian group]]s. It belongs to the field of [[additive combinatorics]], and is named after [[Martin Kneser]], who published it in 1953.<ref>{{cite journal | first=Martin | last=Kneser | title=Abschätzungen der asymptotischen Dichte von Summenmengen | language=German | journal=[[Math. ZeitschrZ.]] | volume=58 | year=1953 | pages=459–484 | zbl=0051.28104 }}

</ref> It may be regarded as an extension of the [[Cauchy–Davenport theorem]], which also concerns sumsets in groups but is restricted to groups whose [[Order (group theory)|order]] is a [[prime number]].<ref name=GR143>{{harvtxt|Geroldinger|Ruzsa|2009|p=143}}</ref>