Skew domino Schensted correspondence and sign-imbalance

Abstract

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 Sjöstrand’s theorems on sign-imbalance of skew shapes.