Two Remarks on Skew Tableaux

Two Remarks on Skew Tableaux

This paper contains two results on the number fσ/τ of standard skew Young tableaux of shape σ/τ . The first concerns generating functions for certain classes of “periodic” shapes related to work of Gessel-Viennot and Baryshnikov-Romik. The second result gives an evaluation of the skew Schur function sλ/μ(x) at x = (1, 1/22k , 1/32k , . . . ) for k = 1, 2, 3 in terms of fσ/τ for a certain skew s...

On the Enumeration of Skew Young Tableaux

Equivariant Littlewood-richardson Skew Tableaux

We give a positive equivariant Littlewood-Richardson rule also discovered independently by Molev. Our proof generalizes a proof by Stembridge of the ordinary Littlewood-Richardson rule. We describe a weight-preserving bijection between our indexing tableaux and the Knutson-Tao puzzles.

Skew Tableaux, Lattice Paths, and Bounded Partitions

We establish a one to one correspondence between a set of certain bounded partitions and a set of two-rowed standard Young tableaux of skew shape. Then we obtain a formula for a number which enumerates these partitions. We give two proofs for this formula, one by applying the above correspondence, the other by using the reflection principle. Finally, we give another expression for this number i...

Two Results on Domino and Ribbon Tableaux

Inspired by the spin-inversion statistic of Schilling, Shimozono and White [8] and Haglund et al. [2] we relate the symmetry of ribbon functions to a result of van Leeuwen, and also describe the multiplication of a domino function by a Schur function.