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The generalized Pascal matrix via the generalized Fibonacci matrix and the generalized Pell matrix

조성훈|이광연
대한수학회 (The Korean Mathematical Society)|2008.03|대한수학회지 (Journal of the KMS)|제45권 제2호|pp. 479-491

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키워드

Riordan matrixPascal matrixFibonacci matrixPell matrix
주제분류수학

초록

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities

Abstract

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities

참고문헌 (9)

  1. R. Brawer, "The linear algebra of the Pascal matrix", Linear Algebra and its Applications, 174, pp.13~23 (1992)
  2. J. Ercolano, "Matrix generators of Pell sequences", FIBONACCI QUARTERLY, 17(1), pp.71~77 (1979)
  3. A. F. Horadam, "Pell identities", FIBONACCI QUARTERLY, 9(3), pp.245~252 (1971)
  4. G. Y. Lee, "Some combinatorial identities via Fibonacci numbers", Discrete Applied Mathematics, 130(3), pp.527~534 (2003)
  5. G. Y. Lee, "Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices", FIBONACCI QUARTERLY, 40(3), pp.203~211 (2002)
  6. P. Peart, "Triple factorization of some Riordan matrices", FIBONACCI QUARTERLY, 31(2), pp.121~128 (1993)
  7. L. W. Shapiro, "The Riordan group", Discrete Applied Mathematics, 34(1), pp.229~239 (1991)
  8. Z. Zhizheng, "The linear algebra of the generalized Pascal matrix", Linear Algebra and its Applications, 250, pp.51~60 (1997)
  9. Z. Zhizheng, "An extension of the generalized Pascal matrix and its algebraic properties", Linear Algebra and its Applications, 271, pp.169~177 (1998)

관련 논문AI추천

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