Skew domino Schensted algorithm and sign-imbalance

Details Skew domino Schensted algorithm and sign-imbalance Skew domino Schensted algorithm and sign-imbalance

2007-11-07

arxiv.org/abs/0711.1035v4

European J. Combin. 31 (2010) 210-229

Mathematics

Combinatorics

22 pages. Final version

Scientific paper

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.

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