Gray Codes for Reflection Groups

J. H. Conway, N. J. A. Sloane and Allan R. Wilks

Graphs and Combinatorics, Vol. 5 (1989), pp. 315-325.

Copyright Springer-Verlag 1989

ABSTRACT: Let G be a finite group generated by reflections. It is shown that the elements of G 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.

Full text: pages 315, 316-320