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Schröder matrix as inverse of Delannoy matrix

2013; Elsevier BV; Volume: 439; Issue: 11 Linguagem: Inglês

10.1016/j.laa.2013.09.044

ISSN

1873-1856

Autores

Sheng-Liang Yang, Sai-Nan Zheng, Shaopeng Yuan, Tian-Xiao He,

Tópico(s)

graph theory and CDMA systems

Resumo

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.

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