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Skew domino Schensted algorithm and sign-imbalance
Using growth diagrams, we define a skew domino Schensted correspondence which
is a domino analogue of the skew Robinson-Schensted correspondence due to Sagan
and Stanley. The color-to-spin property of Shimozono and White is extended. As
an application, we give a simple generating function for the weighted sum of
skew domino tableaux, which is a generalization of Stanley's sign-imbalance
formula. The generating function gives a method to calculate the generalized
sign-imbalance formula. We also extend Sj{\"o}strand's theorems on
sign-imbalance of skew shapes.Comment: 22 pages. Final versio