Graphs and Combinatorics

, Volume 5, Issue 1, pp 315–325

Gray codes for reflection groups


  • J. H. Conway
    • Mathematics DepartmentPrinceton University
  • N. J. A. Sloane
    • Mathematical Sciences Research CenterAT&T Bell Laboratories
  • Allan R. Wilks
    • Mathematical Sciences Research CenterAT&T Bell Laboratories

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


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.

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© Springer-Verlag 1989