In the following from Young Tableaux by Fulton, what happens if our Tableaux has numbers greater than $m$? Fulton gives an example with $m=6$, but according to his definition, we also have a monomial for $m=4$ and yet the numbers $1,2,3,4,5,6$ appear in the tableaux.
Associated to each partition $\lambda$ and integer $m$ such that $\lambda$ has at most $m$ parts (rows), there is an important symmetric polynomial $s_\lambda(x_1,\dots,x_m)$ called a Schur polynomial. These polynomials can be defined quickly using tableaux. To any numbering $T$ of a Young diagram we have a monomial, denoted $x^T$, which is the product of the variables $x_i$ corresponding to the $i$'s that occur in $T$. For the tableau
this monomial is $x_1x_2^3x_3^3x_4^2x_5^4x_6^3$. Formally, $$x^T = \prod_{i=1}^m (x_i)^{\text{number of times $i$ occurs in $T$}}.$$
The Schur polynomial $s_\lambda(x_1,\dots,x_m)$ is the sum $$s_\lambda(x_1,\dots,x_m)=\sum x^T$$ of all monomials coming from tableaux $T$ of shape $\lambda$ using the numbers from $1$ to $m$.