Schur polynomial

A Schur polynomial is a special symmetric polynomial associatedto a partition of an integer, or equivalently to a Young diagram.Schur polynomials also have a power series generalization, theSchur functions.

First we define some notation. Let $\lambda$ be a partition of $n$,and let $T$ be a filling of the Young diagram for $\lambda$. Then by$x^T$ we mean the monomial

$$x^T=\prod _{i=1}^{\mathrm{\infty }}{x}_i^{c_i(T)},$$

where $c_i(T)$ is the number of times the number $i$ appears in thefilling $T$. Since $T$ only has finitely many boxes, the product isfinite. For example, let $\lambda =(3,3,2,2)$, and let $T$ be thefilling