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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hall–Littlewood polynomials ： ウィキペディア英語版 Hall–Littlewood polynomials In mathematics, the Hall–Littlewood polynomials are symmetric functions depending on a parameter ''t'' and a partition λ. They are Schur functions when ''t'' is 0 and monomial symmetric functions when ''t'' is 1 and are special cases of Macdonald polynomials. They were first defined indirectly by Philip Hall using the Hall algebra, and later defined directly by . ==Definition== The Hall–Littlewood polynomial ''P'' is defined by :$P\_\backslash lambda(x\_1,\backslash ldots,x\_n;t)\; =\; \backslash left(\; \backslash prod\_\; \backslash prod\_^\; \backslash fracw\backslash left(x\_1^\backslash cdots\; x\_n^\backslash prod\_\backslash frac\backslash right)\},$ where λ is a partition of at most ''n'' with elements λ''i'', and ''m''(''i'') elements equal to ''i'', and ''S''''n'' is the symmetric group of order ''n''!. As an example, :$P\_(x\_1,x\_2;t)\; =\; x\_1^4\; x\_2^2\; +\; x\_1^2\; x\_2^4\; +\; (1-t)\; x\_1^3\; x\_2^3$ 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「Hall–Littlewood polynomials」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.