1. The pure descent statistic on permutations
- Author
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Jean-Luc Baril, Sergey Kirgizov, Laboratoire d'Electronique, d'Informatique et d'Image UMR CNRS 6306 ( Le2i ), Université de Technologie de Belfort-Montbeliard ( UTBM ) -Centre National de la Recherche Scientifique ( CNRS ) -École Nationale Supérieure d'Arts et Métiers ( ENSAM ) -Université de Bourgogne ( UB ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement, Laboratoire d'Electronique, d'Informatique et d'Image [EA 7508] (Le2i), Université de Technologie de Belfort-Montbeliard (UTBM)-Université de Bourgogne (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, and HESAM Université (HESAM)-HESAM Université (HESAM)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Centre National de la Recherche Scientifique (CNRS)
- Subjects
[ MATH ] Mathematics [math] ,Golomb–Dickman constant ,Distribution (number theory) ,Permutation ,Stirling numbers of the first kind ,Stirling number ,0102 computer and information sciences ,01 natural sciences ,Theoretical Computer Science ,Combinatorics ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Discrete Mathematics and Combinatorics ,[MATH]Mathematics [math] ,0101 mathematics ,Patterns ,Statistic ,Mathematics ,Discrete mathematics ,Mathematics::Combinatorics ,010102 general mathematics ,Descent ,Parity of a permutation ,Gray Code ,010201 computation theory & mathematics ,Random permutation statistics ,Dyck path ,Popularity Fixed Number - Abstract
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.
- Published
- 2017
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