On the K-generalized Fibonacci matrix Qk Original Research Article

The k-generalized Fibonacci sequence {g(k)n} is defined as follows: g(k)1 = … = g(k)k − 2 = 0, g(k)k − 1 = g(k)k = 1, and for n > k greater-or-equal, slanted 2, g(k)n = g(k)n − 1 + g(k)n − 2 + … g(k)n − k. We consider the relationship between g(k)n and 1-factors of a bipartite graph and the eigenvalues of k-generalized Fibonacci matrix Qk for k greater-or-equal, slanted 2. We give some interesting examples in combinatorics and probability with respect to the k-generalized Fibonacci sequence.