\begin{definition}[Definition:Combinatorial Number System]
The '''combinatorial number system''' is a system for representing a positive integer $m$ by a sequence of digits which are the upper coefficient of a sequence of $n$ binomial coefficients for some $n \in \Z_{>0}$:
:$m := k_1 k_2 k_3 \ldots k_n$
where:
:$m = \dbinom {k_1} 1 + \dbinom {k_2} 2 + \dbinom {k_3} 3 + \cdots + \dbinom {k_n} n$
:$0 \le k_1 < k_2 < \cdots < k_n$
\end{definition}