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A determinant of generalized Fibonacci numbers
generalized Fibonacci numbers Cassini’s identity determinant evaluation
2012/4/18
We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of the...
Categorification of the Fibonacci numbers using representations of quivers
Categorification of the Fibonacci numbers representations of quivers Representation Theory
2011/8/31
Abstract: In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the ...
Generalized Fibonacci Numbers and Blackwell's Renewal Theorem
generalized Fibonacci numbers renewal theory
2011/2/25
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell’s renewal theorem we find an approximation to the generalized Fibonacci n...
Generalized Compositions and Weighted Fibonacci Numbers
Compositions Fibonacci numbers Polynomial coefficients
2010/12/8
In this paper we consider particular generalized compositions of a nat-ural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized composit...