6533b82dfe1ef96bd1290b48

RESEARCH PRODUCT

The pure descent statistic on permutations

Jean-luc BarilSergey Kirgizov

subject

[ 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 Number

description

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.

yearjournalcountryeditionlanguage
2017-10-01Discrete Mathematics
https://doi.org/10.1016/j.disc.2017.06.005