Graphs and Combinatorics

, Volume 5, Issue 1, pp 315–325

Gray codes for reflection groups

  • J. H. Conway
  • N. J. A. Sloane
  • Allan R. Wilks
Article

DOI: 10.1007/BF01788686

Cite this article as:
Conway, J.H., Sloane, N.J.A. & Wilks, A.R. Graphs and Combinatorics (1989) 5: 315. doi:10.1007/BF01788686

Abstract

LetG be a finite group generated by reflections. It is shown that the elements ofG can be arranged in a cycle (a “Gray code”) such that each element is obtained from the previous one by applying one of the generators. The case G =A1n yields a conventional binary Gray code. These generalized Gray codes provide an efficient way to run through the elements of any finite reflection group.

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • J. H. Conway
    • 1
  • N. J. A. Sloane
    • 2
  • Allan R. Wilks
    • 2
  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  2. 2.Mathematical Sciences Research CenterAT&T Bell LaboratoriesMurray HillUSA

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