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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Chan, T.M., Patrascu, M.: Counting inversions, offline orthogonal range counting, and related problems. In: Charikar, M. (ed.) Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2010, Austin, Texas, USA, 17–19 January 2010, pp. 161–173. SIAM (2010). https://doi.org/10.1137/1.9781611973075.15
Dietz, P.F.: Optimal algorithms for list indexing and subset rank. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1989. LNCS, vol. 382, pp. 39–46. Springer, Heidelberg (1989). https://doi.org/10.1007/3-540-51542-9_5
Ruskey, F., Williams, A.: An explicit universal cycle for the \((\text{n}-1)\)-permutations of an n-set. ACM Trans. Algorithms 6(3), 45:1–45:12 (2010). https://doi.org/10.1145/1798596.1798598
Rytter, W.: Grammar compression, LZ-encodings, and string algorithms with implicit input. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 15–27. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27836-8_5
Sawada, J., Williams, A.: Solving the sigma-tau problem. http://socs.uoguelph.ca/~sawada/papers/sigmaTauCycle.pdf
Sawada, J., Williams, A.: A Hamilton path for the sigma-tau problem. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, 7–10 January 2018, pp. 568–575 (2018). https://doi.org/10.1137/1.9781611975031.37
Sawada, J., Williams, A., Wong, D.: A surprisingly simple de Bruijn sequence construction. Discret. Math. 339(1), 127–131 (2016). https://doi.org/10.1016/j.disc.2015.08.002
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Rytter, W., Zuba, W. (2019). Syntactic View of Sigma-Tau Generation of Permutations. In: Martín-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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