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In mathematics, the Murnaghan–Nakayama rule is a combinatorial method to compute irreducible character values of the symmetric group.〔Richard Stanley, ''Enumerative Combinatorics, Vol. 2''〕 There are several generalizations of this rule. The Murnaghan–Nakayama is a combinatorial rule for computing the integers χ. Here, λ and ρ are both integer partitions of some number ''k''. Theorem: : where the sum is taken over all ''border-strip'' tableaux of shape λ, and type ρ. That is, each tableau ''T'' is a tableau such that * every row and column is weakly increasing * the integer ''i'' appears ρi times * the set of squares with the number ''i'' form a ''border strip'', that is, it is a connected skew-shape with no 2×2-square. The ''height'', ''ht''(T), is the sum of the heights of the border strips in ''T''. The height of a border strip is one less than the number of rows it touches. ==References== 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「Murnaghan–Nakayama rule」の詳細全文を読む スポンサード リンク
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