Steganographic communication in ordered channels
IH'06 Proceedings of the 8th international conference on Information hiding
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This paper introduces a method for indexing (numbering, ordering) permutations on a given set. It gives algorithms for calculating the index (number, position) of a given permutation and for calculating the permutation indexed by a given integer. Algorithms of this sort are needed for computing with permutations of large sets since the number of these permutations is so large. The algorithms could be particularly useful in simulations requiring random permutations. The algorithm for computing a permutation, given the index, is presented first. The development of the algorithm for computing the index, given the permutation, provides an example of a very high level derivation - since the two algorithms provide inverse processes, the second algorithm simply reverses the roles of input and output in the first algorithm while preserving the fundamental relationship defined there.