## Tokyo Journal of Mathematics

- Tokyo J. Math.
- Volume 39, Number 3 (2017), 729-742.

### Coxeter Elements of the Symmetric Groups Whose Powers Afford the Longest Elements

#### 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.

#### Article information

**Source**

Tokyo J. Math., Volume 39, Number 3 (2017), 729-742.

**Dates**

First available in Project Euclid: 6 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.tjm/1491465734

**Digital Object Identifier**

doi:10.3836/tjm/1491465734

**Mathematical Reviews number (MathSciNet)**

MR3634290

**Zentralblatt MATH identifier**

06727283

**Subjects**

Primary: 20B30: Symmetric groups

Secondary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]

#### Citation

KOSUDA, Masashi. Coxeter Elements of the Symmetric Groups Whose Powers Afford the Longest Elements. Tokyo J. Math. 39 (2017), no. 3, 729--742. doi:10.3836/tjm/1491465734. https://projecteuclid.org/euclid.tjm/1491465734