翻訳と辞書 Words near each other ・ Kostis Palamas ・ Kostis Papagiorgis ・ Kostis Protopapas ・ Kostiuk ・ Kostiukhnivka ・ Kostivere ・ Kostiw ・ Kostić ・ Kostići ・ Kostja Gatnik ・ Kostja Ullmann ・ Kostjukovius ・ Kostka ・ Kostka family ・ Kostka number ・ Kostka polynomial ・ Kostka-Napierski Uprising ・ Kostki Duże ・ Kostki Małe ・ Kostki, Masovian Voivodeship ・ Kostki, Pomeranian Voivodeship ・ Kostki-Pieńki ・ Kostkova ・ Kostkowice ・ Kostkowice, Cieszyn County ・ Kostkowice, Zawiercie County ・ Kostkowo railway station ・ Kostkowo, Pomeranian Voivodeship ・ Kostkowo, Warmian-Masurian Voivodeship ・ Kostków Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kostka polynomial ： ウィキペディア英語版 Kostka polynomial 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 ''K''λμ(''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 ''K''λμ(''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 ''K''λμ(''t'') = ''K''λμ(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 ''P''μ to Schur polynomials ''s''λ: : $s\_\backslash lambda(x\_1,\backslash ldots,x\_n)\; =\backslash sum\_\backslash mu\; K\_(t)P\_\backslash mu(x\_1,\backslash ldots,x\_n;t).\backslash$ 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 : $K\_(t)\; =\; \backslash sum\_\; t^$ 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 ''P''μ) to Schur polynomials ''s''λ: : $s\_\backslash lambda(x\_1,\backslash ldots,x\_n)\; =\backslash sum\_\backslash mu\; K\_(q,t)J\_\backslash mu(x\_1,\backslash ldots,x\_n;q,t)\backslash$ where : $J\_\backslash mu(x\_1,\backslash ldots,x\_n;q,t)\; =\; P\_\backslash mu(x\_1,\backslash ldots,x\_n;q,t)\backslash prod\_(1-q^t^).\backslash$ Kostka numbers are special values of the 1 or 2 variable Kostka polynomials: : $K\_=\; K\_(1)=K\_(0,1).\backslash$ ==Examples== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kostka polynomial」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.