Syntactic View of Sigma-Tau Generation of Permutations
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We give a syntactic view of the Sawada-Williams (σ,τ)-generation of permutations. The corresponding sequence of σ-τ-operations, of length n!-1 is shown to be highly compressible: it has O(n^2 n) bit description. Using this compact description we design fast algorithms for ranking and unranking permutations.
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