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Cyclically reduced word : ウィキペディア英語版 | Cyclically reduced word In mathematics, cyclically reduced word is a concept of combinatorial group theory. Let ''F''(''X'') be a free group. Then a word ''w'' in ''F''(''X'') is said to be ''cyclically reduced'' if and only if every cyclic permutation of the word is reduced. == Properties ==
* Every cyclic shift and the inverse of a cyclically reduced word are cyclically reduced again. * Every word is conjugate to a cyclically reduced word. The cyclically reduced words are minimal-length representatives of the conjugacy classes in the free group. This representative is not uniquely determined, but it is unique up to cyclic shifts (since every cyclic shift is a conjugate element).
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「Cyclically reduced word」の詳細全文を読む
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