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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 Hook length formula ： ウィキペディア英語版 Hook length formula In combinatorial mathematics, the hook-length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram. It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences. == Definitions and statement == Let $\backslash lambda=(\backslash lambda\_1,\backslash ldots,\backslash lambda\_m)$ be a partition of $n$. It is customary to interpret $\backslash lambda$ graphically as a Young diagram, namely a left-justified array of square cells with $m$ rows and $\backslash lambda\_i$ cells in the $i$th row for each $1\backslash le\; i\backslash le\; m$. A standard Young tableau of shape $\backslash lambda$ is a Young diagram of shape $\backslash lambda$ in which each of the $n$ cells contains a distinct integer between 1 and $n$ (i.e., no repetition), such that each row and each column form increasing sequences. For each cell of the Young diagram in coordinates $(i,j)$ (that is, the cell in the $i$th row and $j$th column), the hook $H\_\backslash lambda(i,j)$ is the set of cells $(a,b)$ such that $a=i$ and $b\; \backslash ge\; j$ or $a\; \backslash ge\; i$ and $b=j$. The hook-length $h\_\backslash lambda(i,j)$ is the number of cells in the hook $H\_\backslash lambda(i,j)$. Then the hook-length formula expresses the number of standard Young tableaux of shape $\backslash lambda$, sometimes denoted by $d\_\backslash lambda$, as :$d\_\backslash lambda\; =\; \backslash frac\; ,$ where the product is over all cells $(i,j)$ of $\backslash lambda$. 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「Hook length formula」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.