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Gray codes for reflection groups. (English) Zbl 0684.20036
It is shown that in a finite group generated by reflections R 1 ,···,R n the elements can be arranged in order a 0 ,a 1 ,···,a g-1 so that for each i there is a j such that a i+1 =a i R j (where a g =a 0 ). Such an arrangement is called a Gray code, the classical example being the conventional binary Gray code, which is a Hamiltonian circuit through the n-cube. Specific Gray codes are computed for a number of examples.
Reviewer: F.D.Veldkamp

20H15Other geometric groups, including crystallographic groups
05B45Tessellation and tiling problems
94B25Combinatorial codes
20D60Arithmetic and combinatorial problems on finite groups
20F05Generators, relations, and presentations of groups
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