Evacuation and a geometric construction for Fibonacci tableaux

In 1975, Stanley defined a Fibonacci lattice and in 1988 he introduced the idea of a differential poset. Roby gave an insertion algorithm, analogous to the Schensted correspondence, for mapping a permutation to a pair of Fibonacci tableaux. The main results of this paper are to give an evacuation algorithm for the Fibonacci tableaux that is analogous to the evacuation algorithm on Young tableaux and to describe a geometric construction for the Fibonacci tableaux that is similar to Viennot's geometric construction for Young tableaux.