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The Akiyama-Tanigawa matrix and related combinatorial identities. (English) Zbl 1257.05010

Summary: 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.

MSC:

05A15 Exact enumeration problems, generating functions
05A19 Combinatorial identities, bijective combinatorics
11B73 Bell and Stirling numbers
15B99 Special matrices

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References:

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