A Loopless Implementation of a Gray Code for Signed Permutations

James Korsh, Paul LaFollette, Seymour Lipschutz

Conway, Sloane and Wilks [2] proved the existence of a Gray code for the reflection group $B_n$. The elements of this group are the signed permutations of the set ${1,2,\dots,n}$. Here we give a loopless algorithm which generates a specific Gray code for $B_n$.