Tokyo Journal of Mathematics

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

Masashi KOSUDA

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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


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References

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