The Robinson-Schensted-Knuth correspondence (RSK, see [8] and Corollary 2.5 below) is a bijection between pairs of semi-standard Young tableaux of the same shape and matrices with nonnegative integer entries with prescribed column and row sums. This correspondence plays an important role in the representation theory of the symmetric group and general linear groups, and in the theory of symmetri...

We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics. In this paper K is a field of characteristic zero and all vector spaces are over K. A K[S]-module is a collection of K[Sr]-modules of the symmetric groups Sr. A H(q)-module is a collect...

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 ...

In this paper, explicit formulae for the expectation and the variance of descent functions on random standard Young tableaux are presented. Using these, it is shown that the normalized variance, V/E2, is bounded if and only if a certain inequality relating tableau shape to the descent function holds.

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 ...

We define a class Ln,k of permutations that generalizes alternating (up-down) permutations. We then give bijective proofs of certain pattern-avoidance results for this class. The bijections employed include are a modified form of the RSK insertion algorithm and a different bijection with RSK-like properties. As a special case of our results, we give two bijections between the set A2n(1234) of a...