Reflection factorizations of Singer cycles

J.B. Lewis; V. Reiner; D. Stanton

doi:10.46298/dmtcs.2401

J.B. Lewis ; V. Reiner ; D. Stanton - Reflection factorizations of Singer cycles

dmtcs:2401 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2401

Reflection factorizations of Singer cyclesConference paper

Authors: J.B. Lewis ¹; V. Reiner ¹; D. Stanton ¹

1 School of Mathematics

The number of shortest factorizations into reflections for a Singer cycle in $GL_n(\mathbb{F}_q)$ is shown to be $(q^n-1)^{n-1}$. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given.

https://doi.org/10.46298/dmtcs.2401

Source: HAL:hal-01207611v1

Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)

Section: Proceedings

Published on: January 1, 2014

Imported on: November 21, 2016

Keywords: Singer cycle,Coxeter torus,anisotropic maximal torus,reflection,transvection,factorization,finite general linear group,regular element,q-analogue,higher genus,Coxeter element,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

Funding:

Source : OpenAIRE Graph

RTG in Combinatorics; Funder: National Science Foundation; Code: 1148634
Reflection Group Combinatorics; Funder: National Science Foundation; Code: 1001933

Bibliographic References

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