The study of representations of aane Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any nite Coxeter group. This paper is completely independent of aane Hecke algebra theory and is purely combinatorial. We deene generalized shapes and standard Young tableaux and show that these new objects coincide with the classical ones for root...

Many enumerative problems can be expressed using the scalar product of symmetric functions. As we shall see, we can set up expressions for the generating functions of objects which possess a certain kind of regularity as a scalar product. Two examples of this are k-regular graphs (graphs in which each vertex is of degree k), and secondly we have a class of semi-standard Young tableaux in which ...

The study of standard and generalized Young tableaux has led to interesting results in quite a number of areas of mathematics. These arrays are of importance in the representation theory of the symmetric and general linear groups [12], in invariant theory [7], and in connection with various combinatorial problems [ 11. In addition, many algorithms have been developed that manipulate the tableau...

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...

For any partition, the corresponding Specht module is the sub module of permutation module spanned by the poly-tabloids. The Specht modules for a partition of a positive integer n form a complete list of irreducible representations of permutation group of degree n. The Semi-Standard Young Tableau (SSYT), on n -symbols are one type of combinatorial objects occur naturally in many computational p...

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...