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{\bf Naiomi Cameron and Kendra Killpatrick}
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{\bf Domino Fibonacci Tableaux}
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In 2001, Shimozono and White gave a description of the domino
Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeu\-wen 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 equivalent to Stanley's Fibonacci lattice
$Z(2)$, and define domino Fibonacci tableaux. We give an insertion
algorithm which takes colored permutations to pairs of tableaux
$(P,Q)$ of domino Fibonacci shape. We then define a notion of spin
for domino Fibonacci tableaux for which the insertion algorithm
preserves the color-to-spin property. In addition, we give an
evacuation algorithm for standard domino Fibonacci tableaux which
relates the pairs of tableaux obtained from the domino insertion
algorithm to the pairs of tableaux obtained from Fomin's growth
diagrams.
\bye