# 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

 $x^{T}=\prod_{i=1}^{\infty}x_{i}^{c_{i}(T)},$

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