Abstract
The purpose of this paper is to present a condition for the power of a Coxeter element of $\mathfrak{S}_n$ to become the longest element. To be precise, given a product $C$ of $n-1$ distinct adjacent transpositions of $\mathfrak{S}_n$ in any order, we describe a condition for $C$ such that the $(n/2)$-th power $C^{n/2}$ of $C$ becomes the longest element, in terms of the Amida diagrams.
Citation
Masashi KOSUDA. "Coxeter Elements of the Symmetric Groups Whose Powers Afford the Longest Elements." Tokyo J. Math. 39 (3) 729 - 742, March 2017. https://doi.org/10.3836/tjm/1491465734