## Tokyo Journal of Mathematics

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

Masashi KOSUDA

#### 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

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

Digital Object Identifier
doi:10.3836/tjm/1491465734

Mathematical Reviews number (MathSciNet)
MR3634290

Zentralblatt MATH identifier
06727283

#### 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

#### References

• N. Bourbaki, Groupes et algèbres de Lie IV, V, VI, Hermann, Paris, 1968.
• C. Ceballos, J.-P. Labbé and C. Stump, Subword complexes, cluster complexes, and generalized multiassociahedra, J. Algebraic Combin. 39 (2014), 17–51.
• J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, 1990.