In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.
© 2005 The Fibonnaci Quarterly
A. Benjamin, N. Cameron, J. Quinn, Fibonacci Determinants--A Combinatorial Approach, The Fibonacci Quarterly, Vol. 45, No. 1, 39-55, Feb. 2007