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Schröder matrix as inverse of Delannoy matrix. (English) Zbl 1283.15098

Summary: Using Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy numbers. It turns out that the Delannoy matrix, the Pascal matrix, and the Fibonacci matrix are all special cases of the generalized Delannoy matrices, meanwhile the Schröder matrix and Catalan matrix also arise in involving inverses of the generalized Delannoy matrices. These connections are the focus of our paper. The half of the generalized Delannoy matrix is also considered. In addition, we obtain a combinatorial interpretation for the generalized Fibonacci numbers.

MSC:

15B36 Matrices of integers
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11C20 Matrices, determinants in number theory
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