Skew-standard tableaux with three rows

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...

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...

On the Enumeration of Skew Young Tableaux

Evaluating the Numbers of some Skew Standard Young Tableaux of Truncated Shapes

In this paper the number of standard Young tableaux (SYT) is evaluated by the methods of multiple integrals and combinatorial summations. We obtain the product formulas of the numbers of skew SYT of certain truncated shapes, including the skew SYT ((n + k)r+1, nm−1)/(n − 1)r truncated by a rectangle or nearly a rectangle, the skew SYT of truncated shape ((n+ 1)3, nm−2)/(n− 2)\ (22), and the SYT...