Abstract
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 \(\mathcal {O}(n^2\log n)\) bit description. Using this compact description we design fast algorithms for ranking and unranking permutations.
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Rytter, W., Zuba, W. (2019). Syntactic View of Sigma-Tau Generation of Permutations. In: MartÃn-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_33
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DOI: https://doi.org/10.1007/978-3-030-13435-8_33
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