Search results for "Restricted permutations"

showing 2 items of 2 documents

Gray code for permutations with a fixed number of cycles

2007

AbstractWe give the first Gray code for the set of n-length permutations with a given number of cycles. In this code, each permutation is transformed into its successor by a product with a cycle of length three, which is optimal. If we represent each permutation by its transposition array then the obtained list still remains a Gray code and this allows us to construct a constant amortized time (CAT) algorithm for generating these codes. Also, Gray code and generating algorithm for n-length permutations with fixed number of left-to-right minima are discussed.

Golomb–Dickman constantPolynomial codeRestricted permutationsGenerating algorithms0102 computer and information sciences02 engineering and technology01 natural sciencesTheoretical Computer ScienceGray codeCombinatoricsPermutation[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]0202 electrical engineering electronic engineering information engineeringDiscrete Mathematics and CombinatoricsTransposition arrayComputingMilieux_MISCELLANEOUSMathematicsDiscrete mathematicsSelf-synchronizing codeAmortized analysisMathematics::CombinatoricsParity of a permutation020206 networking & telecommunicationsGray codes010201 computation theory & mathematicsConstant-weight codeMathematicsofComputing_DISCRETEMATHEMATICS
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Gray code for derangements

2004

AbstractWe give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.

021103 operations researchMathematics::CombinatoricsRestricted permutationsApplied Mathematics0211 other engineering and technologiesGenerating algorithms0102 computer and information sciences02 engineering and technologyFixed pointGray codes01 natural sciencesCombinatoricsGray codePermutationDerangement010201 computation theory & mathematicsBounded function[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]Discrete Mathematics and CombinatoricsConstant (mathematics)Rotation (mathematics)Rencontres numbersComputingMilieux_MISCELLANEOUSMathematicsDiscrete Applied Mathematics
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