ON THE K-GENERALIZED FIBONACCI MATRIX Q(K)(ASTERISK)

The k-generalized Fibonacci sequence {g(n)((k))} is defined as follows : g(1)((k)) =...= g(k-2)((k)) = 0, g(k-1)((k)) = g(k)((k)) = 1, and fo r n > k greater than or equal to 2, g(n)((k)) = g(n-1)((k)) + g(n-2)(( k)) +...+ g(n-k)((k)). We consider the relationship between g(n)((k)) and 1-factors of a bipartite graph and the eigenvalues of k-generalize d Fibonacci matrix Q(k) for k greater than or equal to 2. We give some interesting examples in combinatorics and probability with respect to the k-generalized Fibonacci sequence. (C) Elsevier Science Inc., 1997