The pure descent statistic on permutations

Abstract : 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.
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Discrete Mathematics, Elsevier, 2017, 340 (10), pp.2550 - 2558. 〈10.1016/j.disc.2017.06.005〉
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01627131
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Soumis le : mardi 31 octobre 2017 - 18:35:58
Dernière modification le : vendredi 7 décembre 2018 - 16:48:04

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Jean-Luc Baril, Sergey Kirgizov. The pure descent statistic on permutations. Discrete Mathematics, Elsevier, 2017, 340 (10), pp.2550 - 2558. 〈10.1016/j.disc.2017.06.005〉. 〈hal-01627131〉

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