  For a Coxeter group (W,S), a permutation of the set S is called a Coxeter
word and the group element represented by the product is called a Coxeter
element. Moving the first letter to the end of the word is called a rotation
and two Coxeter elements are rotation equivalent if their words can be
transformed into each other through a sequence of rotations and legal
commutations.
  We prove that Coxeter elements are conjugate if and only if they are rotation
equivalent. This was known for some special cases but not for Coxeter groups in
general.
