A freely reduced word is cyclically reduced if its first and last letters are not inverse, with the empty word also allowed. Every cyclic permutation of a nonempty cyclically reduced word is freely reduced, represents a conjugate, and has the same length. Positive powers are freely reduced because no cancellation occurs at copy boundaries.
Articles by others on the same topic
A *cyclically reduced word* is a concept in combinatorial group theory, specifically in the study of free groups and related algebraic structures. A word (or a string of symbols) is said to be cyclically reduced if, when considering its cyclic permutations, it does not contain any instances of an element and its inverse that can be canceled out.