The Akiyama–Tanigawa matrix and related combinatorial identities

In this paper, we define the generalized Akiyama-Tanigawa matrix and investigate its relationship with the r-Stirling numbers of the second kind. Also, we give the generating function for any column or row of the generalized Akiyama-Tanigawa matrix. As a result, we find some new identities about r-S...

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Bibliographic Details
Published in:Linear algebra and its applications 2013-01, Vol.438 (1), p.219-230
Main Author: Rahmani, Mourad
Format: Article
Language:English
Subjects:
Generating function
r-Stirling numbers of the second kind
The Akiyama–Tanigawa matrix
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Summary:In this paper, we define the generalized Akiyama-Tanigawa matrix and investigate its relationship with the r-Stirling numbers of the second kind. Also, we give the generating function for any column or row of the generalized Akiyama-Tanigawa matrix. As a result, we find some new identities about r-Stirling numbers of the second kind. In addition, some applications are given.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2012.07.050