East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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LU-FACTORIZATION OF THE SQUARE-TYPE MATRIX OF THE STIRLING MATRIX

  • Received : 2023.07.18
  • Accepted : 2023.09.28
  • Published : 2023.09.30
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Abstract

Let Sn = [S(i, j)]1≤i,j≤n and S*n = [S(i + j, j)]1≤i,j≤n where S(i, j) is the Stirling number of the second kind. Choi and Jo [On the determinants of the square-type Stirling matrix and Bell matrix, Int. J. Math. Math. Sci. 2021] obtained the diagonal entries of matrix U in the LU-factorization of S*n for calculating the determinant of S*n, where L = Sn. In this paper, we compute the all entries of U in the LU-factorization of matrix S*n. This implies the identities related to Stirling numbers of both kinds.

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References

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