Note on Gray Codes for Permutation Lists

Seymour,Lipschutz ,Jie,Gao ,Dianjun,Wang

Robert Sedgewick [5] lists various Gray codes for the permutations in $S_n$ including the classical algorithm by Johnson and Trotter. Here we give an algorithm which constructs many families of Gray codes for $S_n$, which closely follows the construction of the Binary Reflexive Gray Code for the $n$-cube $Q_n$.