Inhomogeneous basis set of symmetric polynomials defined by tableaux.

A basis set of inhomogeneous symmetric polynomials, denoted by tlambda(z), where z = (z1,....,zn) and lambda = [lambda1,...., lambdan] is a partition, is defined in terms of Young-Weyl standard tableaux or, equivalently, in terms of Gel'fand-Weyl patterns. A number of significant properties of these polynomials are given (together with outlines of proofs) and compared with properties of the well-known basis set of Schur functions, which are homogeneous polynomials. The basis of the ring of symmetric polynomials defined here is shown to be natural for the expansion of inhomogeneous symmetric functions constructed from rising factorials.