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The generalized Fibonomial matrix. (English) Zbl 1184.15021
After defining the generalized Fibonomial matrix and deriving a linear recurrence relation for the generalized Fibonacci coefficients, the author shows that the generalized Fibonomial and Pascal matrices have the same characteristic polynomials i.e. the same eigenvalues. By using matrix methods, explicit and closed formulas for the coefficients and their sums are obtained. In this respect generating functions, properties and combinatorial representations are derived. Additionally, some relationships between determinants of certain matrices and the generalized Fibonacci coefficients are presented. Some applications are also given as illustrative examples.
15B36Matrices of integers
11B39Fibonacci and Lucas numbers, etc.
05A19Combinatorial identities, bijective combinatorics
15A18Eigenvalues, singular values, and eigenvectors
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