Enumeration of Standard Young Tableaux of certain Truncated Shapes

Enumeration of Standard Young Tableaux of certain Truncated Shapes

Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner, rectangular shapes minus a square in the NE corner, and some variations.

Enumeration of Semi { Standard Young Tableaux

Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...

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...

On the Enumeration of Skew Young Tableaux

Tableaux and plane partitions of truncated shapes ( extended abstract )

We consider a new kind of straight and shifted plane partitions/Young tableaux — ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated b...