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In combinatorics, the skew sum and direct sum of permutations are two operations to combine shorter permutations into longer ones. Given a permutation ''π'' of length ''m'' and the permutation ''σ'' of length ''n'', the skew sum of ''π'' and ''σ'' is the permutation of length ''m'' + ''n'' defined by : and the direct sum of ''π'' and ''σ'' is the permutation of length ''m'' + ''n'' defined by : ==Examples== The skew sum of the permutations ''π'' = 2413 and ''σ'' = 35142 is 796835142 (the last five entries are equal to ''σ'', while the first four entries come from shifting the entries of ''π'') while their direct sum is 241379586 (the first four entries are equal to ''π'', while the last five come from shifting the entries of ''σ''). 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「Skew and direct sums of permutations」の詳細全文を読む スポンサード リンク
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