Let us consider an infinit-degree polynomial, $p\left( \mathbf{x} \right)$:
$$p\left( \mathbf{x} \right)=\sum\limits_{\begin{smallmatrix} \mathbf{v}\in {{\mathbb{N}}^{n}} \\ {{v}_{1}}+{{v}_{2}}+...+{{v}_{n}}=m \\ m\in \mathbb{N} \end{smallmatrix}}{\prod\limits_{i=1}^{n}{x_{i}^{{{v}_{i}}}}},$$
where $\mathbb{N}=[0,1,2,...]$ is the set of natural numbers. How to generate all the vectors $\mathbf{v}$ belonging to the integer $m\ge 0$ ?