Coxeter elements of the symmetric groups whose powers afford the longest
  In this article, we first show that in case $n$ is even which Coxeter element in $\mathfrak{S}_{n}$ affords the longest by taking its power to $n/2$. We also show that in case $n$ is odd which Coxeter element affords the longest in $\mathfrak{S}_{n}$. 
Masashi Kosuda
math.GR