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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 Dyson conjecture ： ウィキペディア英語版 Dyson conjecture In mathematics, the Dyson conjecture is a conjecture about the constant term of certain Laurent polynomials, proved by Wilson and Gunson. Andrews generalized it to the q-Dyson conjecture, proved by Zeilberger and Bressoud and sometimes called the Zeilberger–Bressoud theorem. Macdonald generalized it further to more general root systems with the Macdonald constant term conjecture, proved by Cherednik. ==Dyson conjecture== The Dyson conjecture states that the Laurent polynomial :$\backslash prod\; \_(1-t\_i/t\_j)^$ has constant term :$\backslash frac.$ The conjecture was first proved independently by and . later found a short proof, by observing that the Laurent polynomials, and therefore their constant terms, satisfy the recursion relations :$F(a\_1,\backslash dots,a\_n)\; =\; \backslash sum\_^nF(a\_1,\backslash dots,a\_i-1,\backslash dots,a\_n).$ The case ''n'' = 3 of Dyson's conjecture follows from the Dixon identity. and used a computer to find expressions for non-constant coefficients of Dyson's Laurent polynomial. 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「Dyson conjecture」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.