About: Kostka polynomial

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In mathematics, Kostka polynomials, named after the mathematician Carl Kostka, are families of polynomials that generalize the Kostka numbers. They are studied primarily in algebraic combinatorics and representation theory. There are two slightly different versions of them, one called transformed Kostka polynomials. The one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewood polynomials Pμ to Schur polynomials sλ: The Macdonald–Kostka polynomials can be used to relate Macdonald polynomials (also denoted by Pμ) to Schur polynomials sλ: where

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rdf:type	yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Relation100031921 yago:WikicatSymmetricFunctions
rdfs:label	Kostka polynomial (en)
rdfs:comment	In mathematics, Kostka polynomials, named after the mathematician Carl Kostka, are families of polynomials that generalize the Kostka numbers. They are studied primarily in algebraic combinatorics and representation theory. There are two slightly different versions of them, one called transformed Kostka polynomials. The one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewood polynomials Pμ to Schur polynomials sλ: The Macdonald–Kostka polynomials can be used to relate Macdonald polynomials (also denoted by Pμ) to Schur polynomials sλ: where (en)
dcterms:subject	Symmetric functions
Wikipage page ID	22630866 (xsd:integer)
Wikipage revision ID	1038123643 (xsd:integer)
Link from a Wikipage to another Wikipage	Schur polynomial Representation theory Algebraic combinatorics Mathematics Conjecture Macdonald polynomials Kostka number Symmetric functions Alain Lascoux Partition (number theory) Carl Kostka Mathematical proof Hall-Littlewood polynomials Coefficient Marcel-Paul Schützenberger Polynomial Integer Young tableau
Link from a Wikipage to an external page	http://www.aimath.org/WWN/kostka http://garsia.math.yorku.ca/MPWP/qtTEXtables.html http://garsia.math.yorku.ca/MPWP/qtanalogs/sttab/index.html http://www.oup.com/uk/catalogue/%3Fci=9780198504504
sameAs	Kostka polynomial Kostka polynomial Kostka polynomial Kostka polynomial
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:Dead_link dbt:Empty_section dbt:Reflist dbt:Short_description
bot	InternetArchiveBot (en)
date	December 2017 (en)
fix-attempted	yes (en)
has abstract	In mathematics, Kostka polynomials, named after the mathematician Carl Kostka, are families of polynomials that generalize the Kostka numbers. They are studied primarily in algebraic combinatorics and representation theory. The two-variable Kostka polynomials Kλμ(q, t) are known by several names including Kostka–Foulkes polynomials, Macdonald–Kostka polynomials or q,t-Kostka polynomials. Here the indices λ and μ are integer partitions and Kλμ(q, t) is polynomial in the variables q and t. Sometimes one considers single-variable versions of these polynomials that arise by setting q = 0, i.e., by considering the polynomial Kλμ(t) = Kλμ(0, t). There are two slightly different versions of them, one called transformed Kostka polynomials. The one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewood polynomials Pμ to Schur polynomials sλ: These polynomials were conjectured to have non-negative integer coefficients by Foulkes, and this was later proved in 1978 by Alain Lascoux and Marcel-Paul Schützenberger.In fact, they show that where the sum is taken over all semi-standard Young tableaux with shape λ and weight μ.Here, charge is a certain combinatorial statistic on semi-standard Young tableaux. The Macdonald–Kostka polynomials can be used to relate Macdonald polynomials (also denoted by Pμ) to Schur polynomials sλ: where Kostka numbers are special values of the one- or two-variable Kostka polynomials: (en)
prov:wasDerivedFrom	wikipedia-en:Kostka_polynomial?oldid=1038123643&ns=0
page length (characters) of wiki page	3890 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Kostka_polynomial
is Link from a Wikipage to another Wikipage of	List of polynomial topics Hall–Littlewood polynomials Kostka Kostka number Carl Kostka List of special functions and eponyms N! conjecture Kostka-Foulkes polynomial Kostka-Foulkes polynomials Kostka polynomials Kostka–Foulkes polynomial Kostka–Foulkes polynomials Macdonald-Kostka polynomial Macdonald–Kostka polynomial
is Wikipage redirect of	Kostka-Foulkes polynomial Kostka-Foulkes polynomials Kostka polynomials Kostka–Foulkes polynomial Kostka–Foulkes polynomials Macdonald-Kostka polynomial Macdonald–Kostka polynomial
is Wikipage disambiguates of	Kostka
is foaf:primaryTopic of	wikipedia-en:Kostka_polynomial

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