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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… (More)

In 2001, Shimozono and White gave a description of the domino Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeuwen with the " color-to-spin " property, that is, the property that the total color of the permutation equals the sum of the spins of the domino tableaux. In this paper, we describe the poset of domino Fibonacci shapes, an isomorphic… (More)

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