Search results for "Stirling numbers of the first kind"

showing 3 items of 3 documents

Restricted 123-avoiding Baxter permutations and the Padovan numbers

2007

AbstractBaxter studied a particular class of permutations by considering fixed points of the composite of commuting functions. This class is called Baxter permutations. In this paper we investigate the number of 123-avoiding Baxter permutations of length n that also avoid (or contain a prescribed number of occurrences of) another certain pattern of length k. In several interesting cases the generating function depends only on k and is expressed via the generating function for the Padovan numbers.

Discrete mathematicsClass (set theory)Golomb–Dickman constantStirling numbers of the first kindApplied MathematicsPadovan numbersGenerating functionFixed pointCombinatoricsPermutationDiscrete Mathematics and CombinatoricsTree (set theory)Generating treesBaxter permutationsForbidden subsequencesMathematicsDiscrete Applied Mathematics
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Generating restricted classes of involutions, Bell and Stirling permutations

2010

AbstractWe present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles. It generates permutations at each recursive step and slight modifications of it produce generating algorithms for Bell permutations and involutions. Further refinements yield algorithms for these classes of permutations subject to additional restrictions: a given number of cycles or/and fixed points. We obtain, as particular cases, generating algorithms for permutations counted by the Stirling numbers of the first and second kind, even permutations, fixed-point-free involutions and d…

Discrete mathematicsGolomb–Dickman constantMathematics::CombinatoricsStirling numbers of the first kindParity of a permutationTheoretical Computer ScienceCombinatoricsDerangementPermutationComputational Theory and MathematicsRandom permutation statisticsDiscrete Mathematics and CombinatoricsStirling numberGeometry and TopologyRencontres numbersMathematicsMathematicsofComputing_DISCRETEMATHEMATICSEuropean Journal of Combinatorics
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The pure descent statistic on permutations

2017

International audience; We introduce a new statistic based on permutation descents which has a distribution given by the Stirling numbers of the first kind, i.e., with the same distribution as for the number of cycles in permutations. We study this statistic on the sets of permutations avoiding one pattern of length three by giving bivariate generating functions. As a consequence, new classes of permutations enumerated by the Motzkin numbers are obtained. Finally, we deduce results about the popularity of the pure descents in all these restricted sets. (C) 2017 Elsevier B.V. All rights reserved.

[ MATH ] Mathematics [math]Golomb–Dickman constantDistribution (number theory)PermutationStirling numbers of the first kindStirling number0102 computer and information sciences01 natural sciencesTheoretical Computer ScienceCombinatoricsPermutationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONDiscrete Mathematics and CombinatoricsStirling number[MATH]Mathematics [math]0101 mathematicsPatternsStatisticMathematicsDiscrete mathematicsMathematics::Combinatorics010102 general mathematicsDescentParity of a permutationGray Code010201 computation theory & mathematicsRandom permutation statisticsDyck pathPopularity Fixed NumberDiscrete Mathematics
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