Combinatorial number system

Every positive integer

m

has a unique greedy representation

m = (r a _{r}) + (r - 1 a _{r - 1}) + \dots + (s a _{s}), a_{r} > a_{r - 1} > \dots > a_{s} \geq s .

This is also called the binomial representation of

m

at level

r

.

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codex/binomial-representation

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