Growth diagrams, Domino insertion and Sign-imbalance

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{ö}strand's theorems on sign-imbalance of skew shapes.

On domino insertion and Kazhdan--Lusztig cells in type $B_n$

Based on empirical evidence obtained using the {\sf CHEVIE} computer algebra system, we present a series of conjectures concerning the combinatorial description of the Kazhdan--Lusztig cells for type $B_n$ with unequal parameters. These conjectures form a far-reaching extension of the results of Bonnafé and Iancu obtained earlier in the so-called ``asymptotic case''. We give some partial results in support of our conjectures.

On Sjostrand's skew sign-imbalance identity

We give a short proof of Sjostrand's sign-imbalance identity for skew shapes using the domino Cauchy identity.

Some remarks on sign-balanced and maj-balanced posets

Let P be a poset with elements 1,2,...,n. We say that P is sign-balanced if exactly half the linear extensions of P (regarded as permutations of 1,2,...,n) are even permutations, i.e., have an even number of inversions. This concept first arose in the work of Frank Ruskey, who was interested in the efficient generation of all linear extensions of P. We survey a number of techniques for showing that posets are sign-balanced, and more generally, computing their "imbalance." There are close connections with domino tilings and, for certain posets, a "domino generalization" of Schur functions due t…

Young 图中的台球轨道：中缀链、自行车空间与多米诺骨牌平铺

Billiard Orbits in Young Diagrams: Medial Links, Bicycle Spaces, and Domino Tilings

本文研究 Young 图中对角台球轨道的计数，将其与中缀链、二进制自行车空间及多米诺骨牌平铺联系起来，给出精确公式、奇偶性限制及渐近下界。