Some combinatorial identities via 7-matrices
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A matrix A = [aij ] whose entries satisfy the recurrence relation aai-1, j-1 + βai-1,j = aij where α and β are fixed real numbers is calleda 7(α, β)-matrix. In this paper, we prove that every in nite lower triangular7(α, β )-matrix is factorized by generalized Pascal matrix and a Toeplitz matrix. Also, we find some combinatorial identities from the matrix factorizations.
Abstract
A matrix A = [aij ] whose entries satisfy the recurrence relation aai-1, j-1 + βai-1,j = aij where α and β are fixed real numbers is calleda 7(α, β)-matrix. In this paper, we prove that every in nite lower triangular7(α, β )-matrix is factorized by generalized Pascal matrix and a Toeplitz matrix. Also, we find some combinatorial identities from the matrix factorizations.
참고문헌 (11)
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