The partial r-Bell polynomials

In this paper, we show that the r -Stirling numbers of both kinds, the r -Whitney numbers of both kinds, the r -Lah numbers and the r -Whitney-Lah numbers form particular cases of a family of polynomials forming a generalization of the partial Bell polynomials. We deduce the generating functions of...

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Bibliographic Details
Published in:Afrika mathematica 2017-12, Vol.28 (7-8), p.1167-1183
Main Authors: Mihoubi, Miloud, Rahmani, Mourad
Format: Article
Language:English
Subjects:
Applications of Mathematics
Combinatorial analysis
Functions (mathematics)
History of Mathematical Sciences
Mathematical analysis
Mathematics
Mathematics and Statistics
Mathematics Education
Polynomials
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Summary:In this paper, we show that the r -Stirling numbers of both kinds, the r -Whitney numbers of both kinds, the r -Lah numbers and the r -Whitney-Lah numbers form particular cases of a family of polynomials forming a generalization of the partial Bell polynomials. We deduce the generating functions of several restrictions of these numbers. In addition, a new combinatorial interpretations is presented for the r -Whitney numbers and the r -Whitney-Lah numbers.
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-017-0510-z