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<p>In this paper, we first introduce a generalization of Stirling numbers of the first and second kind. Then, using these numbers, we generalize the Stirling matrices of the first and second kind, investigated by Cheon and Kim [Stirling matrix via Pascal matrix, Linear Algebra Appl. 329 (2001) 49–59]. In the following, we will present an LDU-factorization for the multivariate Vandermonde matrix based on the second kind Stirling and multivariate Pascal matrices. Finally, we will obtain some well-known combinatorial identities for the multivariate Stirling numbers of the first and second kind and multivariate binomial coefficients.</p>

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The multivariate pascal, Stirling and Vandermonde matrices

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Morteza Bayat

摘要

In this paper, we first introduce a generalization of Stirling numbers of the first and second kind. Then, using these numbers, we generalize the Stirling matrices of the first and second kind, investigated by Cheon and Kim [Stirling matrix via Pascal matrix, Linear Algebra Appl. 329 (2001) 49–59]. In the following, we will present an LDU-factorization for the multivariate Vandermonde matrix based on the second kind Stirling and multivariate Pascal matrices. Finally, we will obtain some well-known combinatorial identities for the multivariate Stirling numbers of the first and second kind and multivariate binomial coefficients.