CombinatorialNumerals

The combinatorial number system of degree $k$: $n \leftrightarrow$ the strictly decreasing tuple $c_k > \dots > c_1 \ge 0$ with $n = \binom{c_k}{k} + \dots + \binom{c_1}{1}$ — the unranking of $k$-subsets in colexicographic order.

CombinatorialNumerals(k)the system, width $k$, strictly decreasing digits

Typed signatures

Type	Package	Applies
(integer) -> value	numerals	always

Domain: Numeral systems

Examples

Basic #

$3 = \binom{3}{3} + \binom{2}{2} + \binom{1}{1}$

live ↗

In$\mathrm{IntegerDigits}(3, \mathrm{CombinatorialNumerals}(3))$Out$\bigl\lbrack3, 2, 1\bigr\rbrack$

$10 = \binom{5}{2} + \binom{0}{1}$

live ↗

In$\mathrm{IntegerDigits}(10, \mathrm{CombinatorialNumerals}(2))$Out$\bigl\lbrack5, 0\bigr\rbrack$

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Examples	2

See also: IntegerDigits, CombinatorialSystem