We present families of tableaux which interpolate between the classical semi-standard Young and matching field tableaux. Algebraically, this corresponds to SAGBI bases Plücker algebras . show that each such family leads a toric ideal, can be realized as initial hence degeneration for flag variety.

We introduce a combinatorial way of calculating the Hilbert series of bigraded Sn-modules as a weighted sum over standard Young tableaux in the hook shape case. This method is based on Macdonald formula for HallLittlewood polynomial and extends the result of A. Garsia and C. Procesi for the Hilbert series when q = 0. Moreover, we give the way of associating the fillings giving the monomial term...

The Standard Young Tableaux are used to label the basis vectors of the standard or Young Yamanouchi basis of the symmetric group. There is a one to one correspondence between the eigen values of the Complete Set of Commuting Operators-I (CSCO-I) of Symmetric group of degree n (Sn) and the Standard Young Tableaux(SYT). In this paper, a new graphical method to index and retrieve the standard Youn...

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...

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...

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...

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...