In this paper, we consider the Robinson-Schensted correspondence for oscillating tab-leaux and skew oscillating tableaux deened in 15] and 3]. First we give an analogue, for the oscillating tableaux, of the classical geometric construction of Viennot for standard tableaux ((16]). Then, we extend a construction of Sagan and Stanley ((10]), dealing with standard tableaux and skew tableaux, to ded...

A well-known theorem of Frame, Robinson, and, Thrall states that if h is a partition of n, then the number of Standard Young Tableaux of shape h is n! divided by the product of the hook-lengths. We give a new combinatorial proof of this formula by exhibiting a bijection between the set of unsorted Young Tableaux of shape A, and the set of pairs (T, S), where T is a Standard Young Tableau of sha...

Many results involving Schur functions have analogues involving k-Schur functions. Standard strong marked tableaux play a role for k-Schur functions similar to the role standard Young tableaux play for Schur functions. We discuss results and conjectures toward an analogue of the hook-length formula.

Young’s lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young...

Let μ be a partition of k, and T a standard Young tableau of shape μ. McKay, Morse, and Wilf show that the probability a randomly chosen Young tableau of N cells contains T as a subtableau is asymptotic to fμ/k! as N goes to infinity, where fμ is the number of all tableaux of shape μ. We use a random-walk argument to show that the analogous asymptotic probability for randomly chosen Young table...

The widely studied q-polynomial fλ(q), which specializes when q = 1 to fλ, the number of standard Young tableaux of shape λ, has multiple combinatorial interpretations. It represents the dimension of the unipotent representation Sλ q of the finite general linear group GLn(q), it occurs as a special case of the Kostka-Foulkes polynomials, and it gives the generating function for the major index ...