Schröder matrix as inverse of Delannoy matrix
نویسندگان
چکیده
منابع مشابه
Schroder Matrix as Inverse of Delannoy Matrix
Using Riordan arrays, we introduce a generalized Delannoy matrix by weighted Delannoy numbers. It turn 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 o...
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The nth Delannoy number and the nth Schröder number given by D n = n k=0 n k n + k k and S n = n k=0 n k n + k k 1 k + 1 respectively arise naturally from enumerative combinatorics. Let p be an odd prime. We mainly show that p−1 k=1 D k k 2 ≡ 2 −1 p E p−3 (mod p) and p−1 k=1 S k m k ≡ m 2 − 6m + 1 2m 1 − m 2 − 6m + 1 p (mod p), where (−) is the Legendre symbol, E 0 , E 1 , E 2 ,. .. are Euler n...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.09.044