Geodesic
Domino Fibonacci tableaux
The electronic journal of combinatorics, Tome 13 (2006)
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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 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.
DOI : 10.37236/1071
Classification : 05E10, 06A07
Mots-clés : domino Schensted algorithm, color-to-spin property, domino insertion algorithm 
@article{10_37236_1071,
     author = {Naiomi Cameron and Kendra Killpatrick},
     title = {Domino {Fibonacci} tableaux},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1071},
     zbl = {1100.05100},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1071/}
}
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%A Kendra Killpatrick
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Naiomi Cameron; Kendra Killpatrick. Domino Fibonacci tableaux. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1071

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