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Generalized Bell numbers and peirce matrix via Pascal matrix. (English) Zbl 1486.11032

Summary: With the Stirling matrix \(S\) and the Pascal matrix \(T\), we show that \(T^k S(k \geq 0)\) satisfies a type of generalized Stirling recurrence. Then, by expressing the sum of components of each row of \(T^k S\) as \(k\)-Bell number, we investigate properties of \(k\)-Bell numbers as well as \(k\)-Peirce matrix.

MSC:

11B73 Bell and Stirling numbers
15B36 Matrices of integers
11C20 Matrices, determinants in number theory
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References:

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