Skew Domino Schensted Algorithm and Sign-imbalance
نویسنده
چکیده
Using growth diagrams, we define skew domino Schensted algorithm which is a domino analogue of “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. We also extend Sjöstrand’s theorems on sign-imbalance of skew shapes.
منابع مشابه
N ov 2 00 7 SKEW DOMINO SCHENSTED ALGORITHM AND SIGN - IMBALANCE
Using growth diagrams, we define skew domino Schensted algorithm which is a domino analogue of “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-imbalanc...
متن کاملSkew Domino Schensted Algorithm
Using growth diagrams, we define skew domino Schensted algorithm which is a domino analogue of “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-imbalanc...
متن کاملOn the sign-imbalance of skew partition shapes
Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a remarkably simple generalization of the ordinary non-skew formula. The sum of the signs of all standard tableaux ...
متن کاملGrowth diagrams, domino insertion and sign-imbalance
We study some properties of domino insertion, focusing on aspects related to Fomin’s growth diagrams [Fom1, Fom2]. We give a self-contained proof of the semistandard domino-Schensted correspondence given by Shimozono and White [SW], bypassing the connections with mixed insertion entirely. The correspondence is extended to the case of a nonempty 2-core and we give two dual domino-Schensted corre...
متن کاملOn Sjöstrand’s Skew Sign-imbalance Identity
The aim of this note is to give a quick derivation of Theorem 1 using the techniques developed in [1] and the skew domino Cauchy identity. Let Gλ/μ(X; q) = ∑ D q spin(D)xweight(D) be the spin-weight generating function of domino tableaux with shape λ/μ; see for example [1]. Here we will use the convention that spin(D) is equal to half the number of vertical dominoes in D. Though not stated expl...
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تاریخ انتشار 2008