Associated $r$-Dowling numbers and some relatives

Eszter Gyimesi; Gábor Nyul

doi:10.5802/crmath.145

Combinatoire

Associated

r

-Dowling numbers and some relatives

Eszter Gyimesi ¹ ; Gábor Nyul ¹

¹ Institute of Mathematics, University of Debrecen, H–4002 Debrecen P.O.Box 400, Hungary

Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 47-55.

Résumé

In this paper, we introduce a new generalization of Bell numbers, the $s$ -associated $r$ -Dowling numbers by combining two investigational directions. Here, $r$ distinguished elements have to be in distinct blocks, some elements are coloured according to a colouring rule, and the cardinality of certain blocks is bounded from below by $s$ . Along with them, we define some relatives, the $s$ -associated $r$ -Dowling factorials and the $s$ -associated $r$ -Dowling–Lah numbers, when the underlying set is decomposed into cycles or ordered blocks. The study of these numbers is based on their combinatorial meaning, and the exponential generating functions of their sequences derived from the so-called $r$ -compositional formula.

Reçu le : 2019-07-22
Révisé le : 2020-02-17
Accepté le : 2020-11-05
Publié le : 2021-03-01

Zbl

DOI : 10.5802/crmath.145

Classification : 05A15, 05A18, 05A19, 11B73

Affiliations des auteurs :

Eszter Gyimesi ¹ ; Gábor Nyul ¹

¹ Institute of Mathematics, University of Debrecen, H–4002 Debrecen P.O.Box 400, Hungary

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Eszter Gyimesi and G\'abor Nyul},
     title = {Associated $r${-Dowling} numbers and some relatives},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {47--55},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {1},
     year = {2021},
     doi = {10.5802/crmath.145},
     zbl = {1420.11048},
     language = {en},
}

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Eszter Gyimesi; Gábor Nyul. Associated $r$-Dowling numbers and some relatives. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 47-55. doi : 10.5802/crmath.145. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.145/

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