Definition:Combinatorial Number System

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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


Sources