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).

gollark: If I don't add a pronoun search engine to osmarks.tk to search someone's entire internet history for any mention of their pronouns, am I not being accepting?

gollark: If someone insists on certain pronouns and they're either weird/nonstandard (and I don't like them), or they change them all the time, I will ignore them and say "they" or something.

gollark: Yes. I just go by "them" or probably something else if someone asks and I remember.

gollark: https://pronouny.xyz/pronouns/5e3fea8210cd490015d1631d

gollark: so how do I set pronouns?

References

Solitar, Donald; Magnus, Wilhelm; Karrass, Abraham (1976), Combinatorial group theory: presentations of groups in terms of generators and relations, New York: Dover, pp. 33, 188, 212, ISBN 0-486-63281-4

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