Reflection factorizations of Singer cycles

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

Research output: Contribution to journalConference articlepeer-review


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 languageEnglish (US)
Pages (from-to)297-308
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2014
Event26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States
Duration: Jun 29 2014Jul 3 2014

Bibliographical note

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


  • 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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