| dbo: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) |
| dbo:wikiPageExternalLink |
http://dedekind.mit.edu/~rstan/pubs/pubfiles/56.pdf |
| dbo:wikiPageID |
31980740 (xsd:integer) |
| dbo:wikiPageLength |
2570 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1112372655 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Ring_of_symmetric_functions dbr:Basis_(linear_algebra) dbr:Binomial_coefficient dbr:Algebraic_combinatorics dbr:Permutation dbr:Degree_of_a_polynomial dbr:Inversion_(discrete_mathematics) dbr:Mathematics dbr:Symmetric_polynomials dbc:Symmetric_functions dbr:Non-negative dbr:Quasisymmetric_function dbc:Polynomials dbr:Homogeneous_polynomial dbr:Transposition_(mathematics) dbr:Schubert_polynomials dbr:Schur_polynomials dbr:Integer dbr:Factorial dbr:Symmetric_group dbr:One-line_notation |
| dbp:authorlink |
Richard P. Stanley (en) |
| dbp:first |
Richard (en) |
| dbp:last |
Stanley (en) |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Harvs |
| dbp:year |
1984 (xsd:integer) |
| dct:subject |
dbc:Symmetric_functions dbc:Polynomials |
| rdf:type |
yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Polynomial105861855 yago:Relation100031921 yago:WikicatPolynomials yago:WikicatSymmetricFunctions |
| 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) |
| rdfs:label |
Stanley symmetric function (en) |
| owl:sameAs |
freebase:Stanley symmetric function yago-res:Stanley symmetric function wikidata:Stanley symmetric function https://global.dbpedia.org/id/4vdxV |
| prov:wasDerivedFrom |
wikipedia-en:Stanley_symmetric_function?oldid=1112372655&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Stanley_symmetric_function |
| is dbo:wikiPageRedirects of |
dbr:Stanley_symmetric_functions dbr:Stanley_symmetric_polynomial dbr:Stanley_symmetric_polynomials |
| is dbo:wikiPageWikiLink of |
dbr:Schur_polynomial dbr:Quasisymmetric_function dbr:Symmetric_polynomial dbr:Schubert_polynomial dbr:Stanley_symmetric_functions dbr:Stanley_symmetric_polynomial dbr:Stanley_symmetric_polynomials |
| is foaf:primaryTopic of |
wikipedia-en:Stanley_symmetric_function |