About: Sperner family

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In combinatorics, a Sperner family (or Sperner system; named in honor of Emanuel Sperner), or clutter, is a family F of subsets of a finite set E in which none of the sets contains another. Equivalently, a Sperner family is an antichain in the inclusion lattice over the power set of E. A Sperner family is also sometimes called an independent system or irredundant set.

Attributes	Values
rdfs:label	Clutter (matemática) (es) Famille de Sperner (fr) Sperner family (en)
rdfs:comment	En teoría de hipergrafos y combinatoria, el clutter (también llamado Familia de Sperner) de un hipergrafo H definido sobre un conjunto base A, es el hipergrafo ν(H) conformado por todos los subconjuntos de A que "responden" a H, o bien que "contienen" a todas las hiperaristas de H. Formalmente, dado un hipergrafo H definido sobre un conjunto base A, el clutter de H es el operador definido como: Note que H es subconjunto de ν(H), y este es a su vez subconjunto del conjunto potencia del conjunto base, P(A). El clutter de una estructura de hipergrafos G:=(H, K) se define como: (es) En combinatoire, une famille de Sperner (ou système de Sperner), appelé en l'honneur d'Emanuel Sperner, est un hypergraphe (E, F) (c'est-à-dire un ensemble E et un ensemble F de parties de E) dans lequel aucun élément de F ne contient un autre. Formellement, Si X, Y sont dans F et X ≠ Y, alors X n'est pas contenu dans Y et Y n'est pas contenu dans X. De manière équivalente, une famille de Sperner est une antichaîne de l'ensemble des parties (ordonné par l'inclusion) d'un ensemble. (fr) In combinatorics, a Sperner family (or Sperner system; named in honor of Emanuel Sperner), or clutter, is a family F of subsets of a finite set E in which none of the sets contains another. Equivalently, a Sperner family is an antichain in the inclusion lattice over the power set of E. A Sperner family is also sometimes called an independent system or irredundant set. (en)
dct:subject	Families of sets
Wikipage page ID	748730 (xsd:integer)
Wikipage revision ID	1106927357 (xsd:integer)
Link from a Wikipage to another Wikipage	Power set Menger's theorem Minor (graph theory) Antichain Vertex cover Dedekind number Kőnig's theorem (graph theory) Mathematische Zeitschrift Emanuel Sperner Combinatorics Lattice (order) Abstract simplicial complex Family of sets Journal of Combinatorial Theory Free distributive lattice Asymptotic expansion Hypergraph Families of sets Bipartite graph Sperner's theorem Lubell–Yamamoto–Meshalkin inequality The Art of Computer Programming Order ideal
Link from a Wikipage to an external page	http://dml.cz/bitstream/handle/10338.dmlcz/127405/CzechMathJ_48-1998-1_12.pdf http://www-cs-faculty.stanford.edu/~knuth/fasc4a.ps.gz
sameAs	Sperner family Sperner family Sperner family Sperner family Sperner family
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Main dbt:OEIS
has abstract	En teoría de hipergrafos y combinatoria, el clutter (también llamado Familia de Sperner) de un hipergrafo H definido sobre un conjunto base A, es el hipergrafo ν(H) conformado por todos los subconjuntos de A que "responden" a H, o bien que "contienen" a todas las hiperaristas de H. Formalmente, dado un hipergrafo H definido sobre un conjunto base A, el clutter de H es el operador definido como: Note que H es subconjunto de ν(H), y este es a su vez subconjunto del conjunto potencia del conjunto base, P(A). El clutter de una estructura de hipergrafos G:=(H, K) se define como: (es) En combinatoire, une famille de Sperner (ou système de Sperner), appelé en l'honneur d'Emanuel Sperner, est un hypergraphe (E, F) (c'est-à-dire un ensemble E et un ensemble F de parties de E) dans lequel aucun élément de F ne contient un autre. Formellement, Si X, Y sont dans F et X ≠ Y, alors X n'est pas contenu dans Y et Y n'est pas contenu dans X. De manière équivalente, une famille de Sperner est une antichaîne de l'ensemble des parties (ordonné par l'inclusion) d'un ensemble. (fr) In combinatorics, a Sperner family (or Sperner system; named in honor of Emanuel Sperner), or clutter, is a family F of subsets of a finite set E in which none of the sets contains another. Equivalently, a Sperner family is an antichain in the inclusion lattice over the power set of E. A Sperner family is also sometimes called an independent system or irredundant set. Sperner families are counted by the Dedekind numbers, and their size is bounded by Sperner's theorem and the Lubell–Yamamoto–Meshalkin inequality. They may also be described in the language of hypergraphs rather than set families, where they are called clutters. (en)
gold:hypernym	Family
prov:wasDerivedFrom	wikipedia-en:Sperner_family?oldid=1106927357&ns=0
page length (characters) of wiki page	7075 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Sperner_family
is Link from a Wikipage to another Wikipage of	Antichain Curtis Greene Dedekind number Index of combinatorics articles Emanuel Sperner Combinatorics Clutter Clutter (mathematics) Sperner property Matroid Distributive lattice Family of sets Graded poset Thomas Zaslavsky Sperner's theorem Lubell–Yamamoto–Meshalkin inequality Irredundant set Sperner families Sperner system
is Wikipage redirect of	Clutter (mathematics) Irredundant set Sperner families Sperner system
is foaf:primaryTopic of	wikipedia-en:Sperner_family

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