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Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family. It is one of the central results in extremal set theory. It is named after Emanuel Sperner, who published it in 1928. This result is sometimes called Sperner's lemma, but the name "Sperner's lemma" also refers to an unrelated result on coloring triangulations. To differentiate the two results, the result on the size of a Sperner family is now more commonly known as Sperner's theorem.

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rdfs:label	Satz von Sperner (de) 슈페르너의 정리 (ko) Sperner's theorem (en)
rdfs:comment	Der Satz von Sperner ist ein mathematischer Satz, welcher der diskreten Mathematik zugerechnet wird. Emanuel Sperner hat ihn, ausgehend von einer Anregung seines Doktorvaters Otto Schreier, im Jahre 1927 gefunden und 1928 in der Mathematischen Zeitschrift veröffentlicht. Der Satz behandelt den engen Zusammenhang zwischen den Antiketten der Potenzmenge einer endlichen Menge und den sogenannten Binomialkoeffizienten. Er wurde zum Ausgangspunkt eines Zweiges der diskreten Mathematik, der sogenannten Spernertheorie (englisch Sperner theory). Zum Satz von Sperner gibt es verschiedene Beweise und eine große Anzahl von verwandten Resultaten. (de) Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family. It is one of the central results in extremal set theory. It is named after Emanuel Sperner, who published it in 1928. This result is sometimes called Sperner's lemma, but the name "Sperner's lemma" also refers to an unrelated result on coloring triangulations. To differentiate the two results, the result on the size of a Sperner family is now more commonly known as Sperner's theorem. (en) 슈페르너의 정리(독일어: Satz von Sperner, Sperner's theorem, -定理)는 의 기초적인 정리로, 독일 수학자 (독일어: Emmanuel Sperner)가 제시하였다. 이 정리는 수학에서 다루는 가장 기본적인 대상 중 하나인 집합의 개수에 관해 조합론적 기법을 전개할 수 있음을 보였다는 점에서 의미가 있다. (ko)
dcterms:subject	Articles containing proofs Factorial and binomial topics Families of sets
Wikipage page ID	748844 (xsd:integer)
Wikipage revision ID	1110420126 (xsd:integer)
Link from a Wikipage to another Wikipage	Power set Antichain Articles containing proofs Factorial and binomial topics Mathematische Zeitschrift Emanuel Sperner Sperner property of a partially ordered set Cut-the-knot Erdős–Ko–Rado theorem Finite set Hasse diagram Dilworth's theorem List of continuity-related mathematical topics Family of sets Graded poset Journal of Combinatorial Theory Families of sets Bulletin of the AMS Sperner's lemma Extremal combinatorics Lubell–Yamamoto–Meshalkin inequality Partially ordered Elementary symmetric function Sperner family Gaussian coefficient Partial order width
Link from a Wikipage to an external page	http://www.renyi.hu/~p_erdos/1945-04.pdf http://www.cut-the-knot.org/pigeonhole/sperner.shtml http://michaelnielsen.org/polymath1/index.php%3Ftitle=Sperner%27s_theorem
sameAs	Sperner's theorem Sperner's theorem Sperner's theorem Sperner's theorem Sperner's theorem Sperner's theorem Sperner's theorem Sperner's theorem
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first	K. (en)
id	S/s130500 (en)
last	Engel (en)
title	Sperner theorem (en)
has abstract	Der Satz von Sperner ist ein mathematischer Satz, welcher der diskreten Mathematik zugerechnet wird. Emanuel Sperner hat ihn, ausgehend von einer Anregung seines Doktorvaters Otto Schreier, im Jahre 1927 gefunden und 1928 in der Mathematischen Zeitschrift veröffentlicht. Der Satz behandelt den engen Zusammenhang zwischen den Antiketten der Potenzmenge einer endlichen Menge und den sogenannten Binomialkoeffizienten. Er wurde zum Ausgangspunkt eines Zweiges der diskreten Mathematik, der sogenannten Spernertheorie (englisch Sperner theory). Zum Satz von Sperner gibt es verschiedene Beweise und eine große Anzahl von verwandten Resultaten. (de) Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family. It is one of the central results in extremal set theory. It is named after Emanuel Sperner, who published it in 1928. This result is sometimes called Sperner's lemma, but the name "Sperner's lemma" also refers to an unrelated result on coloring triangulations. To differentiate the two results, the result on the size of a Sperner family is now more commonly known as Sperner's theorem. (en) 슈페르너의 정리(독일어: Satz von Sperner, Sperner's theorem, -定理)는 의 기초적인 정리로, 독일 수학자 (독일어: Emmanuel Sperner)가 제시하였다. 이 정리는 수학에서 다루는 가장 기본적인 대상 중 하나인 집합의 개수에 관해 조합론적 기법을 전개할 수 있음을 보였다는 점에서 의미가 있다. (ko)
prov:wasDerivedFrom	wikipedia-en:Sperner's_theorem?oldid=1110420126&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Sperner's_theorem
is Link from a Wikipage to another Wikipage of	Q-analog Emanuel Sperner Envy-freeness Combinatorics: The Rota Way Kruskal–Katona theorem Sperner property of a partially ordered set Erdős–Ko–Rado theorem Dilworth's theorem Family of sets Graded poset Proofs from THE BOOK Extremal Problems For Finite Sets Extremal combinatorics List of theorems Littlewood–Offord problem Lubell–Yamamoto–Meshalkin inequality Sperner family Sperner theorem Sperner theory
is Wikipage redirect of	Sperner theorem Sperner theory
is known for of	Emanuel Sperner
is known for of	Emanuel Sperner
is foaf:primaryTopic of	wikipedia-en:Sperner's_theorem

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