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In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley in his study of the symmetric group of permutations. reduced decompositions. (Here denotes the binomial coefficient n(n − 1)/2 and ! denotes the factorial.)

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Polynomial105861855 yago:Relation100031921 yago:WikicatPolynomials yago:WikicatSymmetricFunctions
rdfs:label	Stanley symmetric function (en)
rdfs:comment	In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley in his study of the symmetric group of permutations. reduced decompositions. (Here denotes the binomial coefficient n(n − 1)/2 and ! denotes the factorial.) (en)
dcterms:subject	Symmetric functions Polynomials
Wikipage page ID	31980740 (xsd:integer)
Wikipage revision ID	1112372655 (xsd:integer)
Link from a Wikipage to another Wikipage	Ring of symmetric functions Basis (linear algebra) Binomial coefficient Algebraic combinatorics Permutation Degree of a polynomial Inversion (discrete mathematics) Mathematics Symmetric polynomials Symmetric functions Non-negative Quasisymmetric function Polynomials Homogeneous polynomial Transposition (mathematics) Schubert polynomials Schur polynomials Integer Factorial Symmetric group One-line notation
Link from a Wikipage to an external page	http://dedekind.mit.edu/~rstan/pubs/pubfiles/56.pdf
sameAs	Stanley symmetric function Stanley symmetric function Stanley symmetric function Stanley symmetric function
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvs
authorlink	Richard P. Stanley (en)
first	Richard (en)
last	Stanley (en)
year	1984 (xsd:integer)
has abstract	In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley in his study of the symmetric group of permutations. Formally, the Stanley symmetric function Fw(x1, x2, ...) indexed by a permutation w is defined as a sum of certain fundamental quasisymmetric functions. Each summand corresponds to a reduced decomposition of w, that is, to a way of writing w as a product of a minimal possible number of adjacent transpositions. They were introduced in the course of Stanley's enumeration of the reduced decompositions of permutations, and in particular his proof that the permutation w0 = n(n − 1)...21 (written here in one-line notation) has exactly reduced decompositions. (Here denotes the binomial coefficient n(n − 1)/2 and ! denotes the factorial.) (en)
prov:wasDerivedFrom	wikipedia-en:Stanley_symmetric_function?oldid=1112372655&ns=0
page length (characters) of wiki page	2570 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stanley_symmetric_function
is Link from a Wikipage to another Wikipage of	Schur polynomial Quasisymmetric function Symmetric polynomial Schubert polynomial Stanley symmetric functions Stanley symmetric polynomial Stanley symmetric polynomials
is Wikipage redirect of	Stanley symmetric functions Stanley symmetric polynomial Stanley symmetric polynomials
is foaf:primaryTopic of	wikipedia-en:Stanley_symmetric_function

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