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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 Stirling numbers of the first kind ： ウィキペディア英語版 Stirling numbers of the first kind In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles (counting fixed points as cycles of length one). (The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices. This article is devoted to specifics of Stirling numbers of the first kind. Identities linking the two kinds appear in the article on Stirling numbers in general.) ==Definitions== The original definition of Stirling numbers of the first kind was algebraic. These numbers, usually written ''s''(''n'', ''k''), are signed integers whose sign, positive or negative, depends on the parity of ''n'' − ''k''. Afterwards, the absolute values of these numbers, |''s''(''n'', ''k'')|, which are known as unsigned Stirling numbers of the first kind, were found to count permutations, so in combinatorics the (signed) Stirling numbers of the first kind, ''s''(''n'', ''k''), are often defined as counting numbers multiplied by a sign factor. That is the approach taken on this page. Most identities on this page are stated for unsigned Stirling numbers. Note that the notations on this page are not universal. 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「Stirling numbers of the first kind」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.