Evaluating some determinants of matrices with recursive entries
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Let α = (α1,α2,···) and β=(β1,β2,···) be two sequences with α1=β1 and k and n be natural numbers. We denote by A_(α,β)^(k,±)(n) the matrix of order n with coefficients α_(i,j) by setting α_(i,1)=α_(i),α_(i,1)=β_(i) for 1≤i≤n and <수식> for 2≤i,j≤n. The aim of this paper is to study the determinants of such matrices related to certain sequences αand β. and some natural numbers k.
Abstract
Let α = (α1,α2,···) and β=(β1,β2,···) be two sequences with α1=β1 and k and n be natural numbers. We denote by A_(α,β)^(k,±)(n) the matrix of order n with coefficients α_(i,j) by setting α_(i,1)=α_(i),α_(i,1)=β_(i) for 1≤i≤n and <수식> for 2≤i,j≤n. The aim of this paper is to study the determinants of such matrices related to certain sequences αand β. and some natural numbers k.
참고문헌 (3)
- R. Bacher, "Determinants of matrices related to the Pascal triangle", J. Theor. Nombres Bordeaux, 14(1), pp.19~41 (2002)
- C. Krattenthaler, "Advanced determinant calculus", Sem. Lothar. Combin, 42, pp.67~ (1999)
- C. Krattenthaler, "Evaluations of some determinants of matrices related to the Pascal triangle", Sem. Lothar. Combin., 47, pp.19~ (2002)