Years and Authors of Summarized Original Work
1962; Trotter
1963; Johnson
1977; Sedgewick
2008; Sekine, Yamanaka, Nakano
Problem Definition
Permutation Enumeration
Let S n be the set of permutations of [n] = { 1, 2, …, n}. We write a permutation as a sequence of elements in [n] such that each element appears exactly once. A permutation enumeration is to list all permutations in S n . For example, there are 24 permutations of [4]: 1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321. The enumeration of permutations is a basic and long-standing enumeration problem, and it was surveyed by Sedgewick [8].
Note that the above example lists all the permutations of [4], and we have listed them in lexicographic order, which is the most natural way to enumerate them. The purpose of this paper is to introduce representative methods for enumeration problems by showing how these methods are applied to...
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Arimura H, Uno T (2007) An efficient polynomial space and polynomial delay algorithm for enumeration of maximal motifs in a sequence. J Comb Optim 13:243–262
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Yamanaka, K. (2016). Permutation Enumeration. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_735
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