Geodesic
A color-to-spin domino Schensted algorithm
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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We describe the domino Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeuwen. We place this algorithm in the context of Haiman's mixed and left-right insertion algorithms and extend it to colored words. It follows easily from this description that total color of a colored word maps to the sum of the spins of a pair of $2$-ribbon tableaux. Various other properties of this algorithm are described, including an alternative version of the Littlewood-Richardson bijection which yields the $q$-Littlewood-Richardson coefficients of Carré and Leclerc. The case where the ribbon tableau decomposes into a pair of rectangles is worked out in detail. This case is central in recent work by D. White on the number of even and odd linear extensions of a product of two chains.
DOI : 10.37236/1565
Classification : 05E10, 05E05
Mots-clés : domino Schensted algorithm, insertion algorithms, spins, 2-ribbon tableaux, Littlewood-Richardson bijection, \(q\)-Littlewood-Richardson coefficients 
@article{10_37236_1565,
     author = {Mark Shimozono and Dennis E. White},
     title = {A color-to-spin domino {Schensted} algorithm},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {1},
     doi = {10.37236/1565},
     zbl = {0965.05095},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1565/}
}
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Mark Shimozono; Dennis E. White. A color-to-spin domino Schensted algorithm. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1565

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