\begin{definition}[Definition:Binomial Coefficient/Multiindices]
Let $k = \sequence {k_j}_{j \mathop \in J}$ and $\ell = \sequence {\ell_j}_{j \mathop \in J}$ be multiindices.
Let $\ell \le k$.
Then $\dbinom k \ell$ is defined as:
:$\ds \binom k \ell = \prod_{j \mathop \in J} \binom {k_j} {\ell_j}$
Note that since by definition only finitely many of the $k_j$ are non-zero, the product in the definition of $\dbinom k \ell$ is convergent.
Category:Definitions/Binomial Coefficients
Category:Definitions/Polynomial Theory
\end{definition}