k-ribbon Fibonacci tableaux

We extend the notion of k -ribbon tableaux to the Fibonacci lattice, a differential poset defined by R. Stanley in 1975. Using this notion, we describe an insertion algorithm that takes k -colored permutations to pairs of k -ribbon Fibonacci tableaux of the same shape, and we demonstrate a color-to-spin property, similar to that described by Shimozono and White for ribbon tableaux. We describe a geometric interpretation of k -ribbon Fibonacci tableaux and use this interpretation to describe a notion of P equivalence for k -ribbon Fibonacci tableaux. In addition, we give an evacuation algorithm which relates the pair of k -ribbon Fibonacci tableaux obtained through the insertion algorithm to the pair of k -ribbon Fibonacci tableaux obtained using Fomin’s growth diagrams.