a nonnegative integer $n$ with at most $m$ parts is $\lambda=(\lambda_1,\lambda_2,\dots,\lambda_m)$ with $\lambda_1\geq \lambda_2 \geq \cdots \geq \lambda_m\geq 0$ and $\sum_{i=1}^m \lambda_i = n$. This is denoted by $\lambda\vdash n$. The number of positive parts of $\lambda$ is denoted by $\ell(\lambda)$. The [**Young diagram**]{} associated to $\lambda$ is an arrangement of boxes with $\lambda_i$ boxes in the $i$-th row, with rows aligned at the left. Given partitions $\mu$ and $\lambda$ such that the Young diagram of $\lambda$ is contained in the Young diagram of $\mu$, the [**skew shape**]{} $\mu/\lambda$ is the Young diagram consisting of boxes in $\mu$ which are not in $\lambda$. A [**semistandard Young tableau**]{} is a filling of a Young diagram with positive integers such that entries are weakly increasing along each row and strictly increasing along each column. Let $\operatorname{SSYT}^{[m]}(\mu/\lambda)$ denote the set of all semistandard Young tableaux of shape $\mu/\lambda$ with fillings from $[m]=\{1,\dots,m\}$.

Let $\x = (x_1,\ldots,x_m)$. The [**Schur polynomial**]{} in $m$ variables indexed by $\lambda\vdash n$ is $$s_{\lambda}(\x)=\sum_{T\in\operatorname{SSYT}^{[m]}(\lambda)} \x^T,$$ where $\x^T= x_1^{d_1(T)}\cdots x_m^{d_m(T)}$ such that $d_i(T)$ is the number of times $i$ appears in $T$.

\[ex:(3)\] Consider the partition $\lambda=(3,0,0)\vdash 3$. Let $m=3$ and $\x = (x_1,x_2,x_3)$. The semistandard Young tableaux are $$\ytableausetup{smalltableaux}
