# Schur polynomial

A *Schur polynomial* is a special symmetric polynomial associated
to a partition of an integer, or equivalently to a Young diagram.
Schur polynomials also have a power series^{} generalization^{}, the
*Schur 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 the
filling $T$. Since $T$ only has finitely many boxes, the product^{} is
finite. For example, let $\lambda =(3,3,2,2)$, and let $T$ be the
filling