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Schröder matrix as inverse of Delannoy matrix
Authors:Sheng-liang Yang  Sai-nan Zheng  Shao-peng Yuan  Tian-Xiao He
Institution:1. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050, Gansu, PR China;2. Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702, USA
Abstract:Using Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy numbers. It turns out that Delannoy matrix, Pascal matrix, and Fibonacci matrix are all special cases of the generalized Delannoy matrices, meanwhile 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 generalized Delannoy matrix is also considered. In addition, we obtain a combinatorial interpretation for the generalized Fibonacci numbers.
Keywords:05A05  05A15  05A10  15A09  15A36
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