Generating indecomposable permutations |
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Authors: | Andrew King |
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Institution: | Department of Computer Science, McGill University, Montreal, Que., Canada |
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Abstract: | An indecomposable permutation π on n] is one such that π(m])=m] for no m<n. We consider indecomposable permutations and give a new, inclusive enumerative recurrence for them. This recurrence allows us to generate all indecomposable permutations of length n in transposition Gray code order, in constant amortized time (CAT). We also present a CAT generation algorithm for indecomposable permutations which is based on the Johnson-Trotter algorithm for generating all permutations of length n. The question of whether or not there exists an adjacent transposition Gray code for indecomposable permutations remains open. |
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Keywords: | Gray code Combinatorial generation Indecomposable permutation CAT algorithm |
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