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
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.6$: Binomial Coefficients: Exercise $56$