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Skew domino Schensted algorithm and sign-imbalance

Abstract : Using growth diagrams, we define a skew domino Schensted algorithm which is a domino analogue of the "Robinson-Schensted algorithm for skew tableaux'' 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 a weighted sum of skew domino tableaux whose special case is a generalization of Stanley's sign-imbalance formula. The generating function gives a method to calculate the generalized sign-imbalance formula.
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Jang Soo Kim. Skew domino Schensted algorithm and sign-imbalance. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.117-128, ⟨10.46298/dmtcs.3623⟩. ⟨hal-01185158⟩



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