Cyclically reduced word
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Script error: No such module "Unsubst". In mathematics, cyclically reduced word is a concept of combinatorial group theory.
Let F(X)Script error: No such module "Check for unknown parameters". be a free group. Then a word in F(X)Script error: No such module "Check for unknown parameters". 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).
References
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