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Gray codes for reflection groups

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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 =A n1 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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Authors and Affiliations

  1. Mathematics Department, Princeton University, 08540, Princeton, NJ, USA

    J. H. Conway

  2. Mathematical Sciences Research Center, AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    N. J. A. Sloane & Allan R. Wilks

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  1. J. H. Conway
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  2. N. J. A. Sloane
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  3. Allan R. Wilks
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Conway, J.H., Sloane, N.J.A. & Wilks, A.R. Gray codes for reflection groups. Graphs and Combinatorics 5, 315–325 (1989). https://doi.org/10.1007/BF01788686

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