STRINGS, PATHS AND STANDARD TABLEAUX

Standard Young tableaux and colored Motzkin paths

In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the n-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length n. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most 2d+ 1 rows and the set of ...

Osculating Paths and Oscillating Tableaux

The combinatorics of certain tuples of osculating lattice paths is studied, and a relationship with oscillating tableaux is obtained. The paths being considered have fixed start and end points on respectively the lower and right boundaries of a rectangle in the square lattice, each path can take only unit steps rightwards or upwards, and two different paths within a tuple are permitted to share...

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...

Polygon Dissections and Standard Young Tableaux

A simple bijection is given between dissections of a convex n gon with d diagonals not intersecting in their interiors and standard Young tableaux of shape d d n d Partially supported by National Science Foundation grant DMS For d n let f n d be the number of ways to draw d diagonals in a convex n gon such that no two diagonals intersect in their interior For instance f n n is just the Catalan ...

Some strings in Dyck paths