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: What? It's developed in seemingly old-style PHP (source: API docs), it's claimed that someone managed to find the source, it's quite old, and it's been built up over time.

gollark: It wouldn't surprise me if DC was horrendously insecure.

gollark: From duckduckgo.

gollark: ```Data miningData mining is the process of discovering patterns in large data sets involving methods at the intersection of machine learning, statistics, and database systems.```

gollark: That's not what datamining means.

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.