Syntactic View of Sigma-Tau Generation of Permutations

We give a syntactic view of the Sawada-Williams $(\sigma ,\tau )$-generation of permutations. The corresponding sequence of $\sigma -\tau$-operations, of length $n!-1$ is shown to be highly compressible: it has $O(n^2\log n)$ bit description. Using this compact description we design fast algorithms for ranking and unranking permutations.