Coxeter elements of the symmetric groups whose powers afford the longest

Abstract

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 ${\mathfrak{S}}_n$.

13 pages