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Kostka_number abstract "In mathematics, the Kostka number Kλμ (depending on two integer partitions λ and μ) is a non-negative integer that is equal to the number of semistandard Young tableaux of shape λ and weight μ. They were introduced by the mathematician Carl Kostka in his study of symmetric functions (Kostka (1882)).For example, if λ = (3, 2) and μ = (1, 1, 2, 1), the Kostka number Kλμ counts the number of ways to fill a left-aligned collection of boxes with 3 in the first row and 2 in the second row with 1 copy of the number 1, 1 copy of the number 2, 2 copies of the number 3 and 1 copy of the number 4 such that the entries increase along columns and do not decrease along rows. The three such tableaux are shown at right, and K(3, 2) (1, 1, 2, 1) = 3.".
Kostka_number thumbnail Semistandard_Young_tableaux_of_shape_(3,_2)_and_weight_(1,_1,_2,_1).png?width=300.
Kostka_number wikiPageExternalLink ?IDDOC=259790.
Kostka_number wikiPageExternalLink ?ci=9780198504504.
Kostka_number wikiPageID "22606041".
Kostka_number wikiPageLength "6186".
Kostka_number wikiPageOutDegree "23".
Kostka_number wikiPageRevisionID "678609031".
Kostka_number wikiPageWikiLink Carl_Kostka.
Kostka_number wikiPageWikiLink Category:Integer_sequences.
Kostka_number wikiPageWikiLink Category:Symmetric_functions.
Kostka_number wikiPageWikiLink Combinatorics.
Kostka_number wikiPageWikiLink Crelles_Journal.
Kostka_number wikiPageWikiLink Dominance_order.
Kostka_number wikiPageWikiLink General_linear_group.
Kostka_number wikiPageWikiLink Hook-length_formula.
Kostka_number wikiPageWikiLink Irreducible_representation.
Kostka_number wikiPageWikiLink Kostka_polynomial.
Kostka_number wikiPageWikiLink Linear_combination.
Kostka_number wikiPageWikiLink Mathematics.
Kostka_number wikiPageWikiLink Natural_number.
Kostka_number wikiPageWikiLink Non-negative_integer.
Kostka_number wikiPageWikiLink Partition_(number_theory).
Kostka_number wikiPageWikiLink Permutation_module.
Kostka_number wikiPageWikiLink Representation_theory.
Kostka_number wikiPageWikiLink Ring_of_symmetric_functions.
Kostka_number wikiPageWikiLink Schur_polynomial.
Kostka_number wikiPageWikiLink Semistandard_Young_tableaux.
Kostka_number wikiPageWikiLink Weight_(representation_theory).
Kostka_number wikiPageWikiLink Weight_space.
Kostka_number wikiPageWikiLink Yamanouchi_tableau.
Kostka_number wikiPageWikiLink Young_diagram.
Kostka_number wikiPageWikiLink Young_tableau.
Kostka_number wikiPageWikiLink File:Semistandard_Young_tableaux_of_shape_(3,_2)_and_weight_(1,_1,_2,_1).png.
Kostka_number wikiPageWikiLinkText "Kostka number".
Kostka_number authorlink "Bruce Sagan".
Kostka_number first "Bruce E.".
Kostka_number hasPhotoCollection Kostka_number.
Kostka_number id "s/s120040".
Kostka_number last "Sagan".
Kostka_number title "Schur functions in algebraic combinatorics".
Kostka_number wikiPageUsesTemplate Template:Citation.
Kostka_number wikiPageUsesTemplate Template:Harvtxt.
Kostka_number wikiPageUsesTemplate Template:Reflist.
Kostka_number wikiPageUsesTemplate Template:Springer.
Kostka_number subject Category:Integer_sequences.
Kostka_number subject Category:Symmetric_functions.
Kostka_number hypernym Integer.
Kostka_number type Function.
Kostka_number type Polynomial.
Kostka_number comment "In mathematics, the Kostka number Kλμ (depending on two integer partitions λ and μ) is a non-negative integer that is equal to the number of semistandard Young tableaux of shape λ and weight μ.".
Kostka_number label "Kostka number".
Kostka_number sameAs Nombre_de_Kostka.
Kostka_number sameAs m.05zmppq.
Kostka_number sameAs Q6433560.
Kostka_number sameAs Q6433560.
Kostka_number wasDerivedFrom Kostka_number?oldid=678609031.
Kostka_number depiction Semistandard_Young_tableaux_of_shape_(3,_2)_and_weight_(1,_1,_2,_1).png.
Kostka_number isPrimaryTopicOf Kostka_number.