Reflection factorizations of Singer cycles

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

Reflection factorizations of Singer cycles

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

School of Mathematics

Research output: Contribution to journal › Conference article › peer-review

Abstract

The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qⁿ - 1)ⁿ-¹. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given.

Original language	English (US)
Pages (from-to)	297-308
Number of pages	12
Journal	Discrete Mathematics and Theoretical Computer Science
State	Published - 2014
Event	26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States Duration: Jun 29 2014 → Jul 3 2014

Bibliographical note

Funding Information:
Work partially supported by NSF grants DMS-1148634 and DMS-1001933.

Keywords

Anisotropic maximal torus
Coxeter element
Coxeter torus
Factorization
Finite general linear group
Higher genus
Q-analogue
Reflection
Regular element
Singer cycle
Transvection

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@article{a120529027f64beea7664f1933a5b26f,

title = "Reflection factorizations of Singer cycles",

abstract = "The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn - 1)n-1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given.",

keywords = "Anisotropic maximal torus, Coxeter element, Coxeter torus, Factorization, Finite general linear group, Higher genus, Q-analogue, Reflection, Regular element, Singer cycle, Transvection",

author = "Lewis, {J. B.} and V. Reiner and D. Stanton",

note = "Funding Information: Work partially supported by NSF grants DMS-1148634 and DMS-1001933.; 26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 ; Conference date: 29-06-2014 Through 03-07-2014",

year = "2014",

language = "English (US)",

pages = "297--308",

journal = "Discrete Mathematics and Theoretical Computer Science",

issn = "1462-7264",

publisher = "Maison de l'informatique et des mathematiques discretes",

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TY - JOUR

T1 - Reflection factorizations of Singer cycles

AU - Lewis, J. B.

AU - Reiner, V.

AU - Stanton, D.

N1 - Funding Information: Work partially supported by NSF grants DMS-1148634 and DMS-1001933.

PY - 2014

Y1 - 2014

N2 - The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn - 1)n-1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given.

AB - The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn - 1)n-1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given.

KW - Anisotropic maximal torus

KW - Coxeter element

KW - Coxeter torus

KW - Factorization

KW - Finite general linear group

KW - Higher genus

KW - Q-analogue

KW - Reflection

KW - Regular element

KW - Singer cycle

KW - Transvection

UR - http://www.scopus.com/inward/record.url?scp=85082953195&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85082953195&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85082953195

SN - 1462-7264

SP - 297

EP - 308

JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

T2 - 26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014

Y2 - 29 June 2014 through 3 July 2014

ER -

Reflection factorizations of Singer cycles

Abstract

Bibliographical note

Keywords

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