Definition:Combinatorial Number System

Definition
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:
 * $m = \dbinom {k_1} 1 + \dbinom {k_2} 2 + \dbinom {k_3} 3 + \cdots + \dbinom {k_n} n$
 * $0 \le k_1 < k_2 < \cdots < k_n$

Also see

 * Numbers Expressed as Sums of Binomial Coefficients