WeakCompositions

The weak compositions of $n$ into $k$ parts: ordered sequences of $k$ non-negative integers summing to $n$, unlike IntegerCompositions where every part must be positive.

✓ checked against that system · ! checked, with disagreements (hover a chip)OEISA178300✓↗

WeakCompositions(n, k)the $\binom{n+k-1}{k-1}$ sequences of $k$ non-negative parts summing to $n$

CombinatoricaCompositions[n, k]

Typed signatures

Type	Package	Applies
(integer<0..>, integer<0..>) -> indexed_collection<list<integer>>	combinatorics	always

Domain: Collections

Examples

Basic #

$\binom{6}{2} = 15$

live ↗

In$\mathrm{Count}(\mathrm{WeakCompositions}(4, 3))$Out$15$

Parts may be zero

live ↗

In$\mathrm{Take}(\mathrm{WeakCompositions}(2, 2), 3)$Out$\bigl\lbrack\bigl\lbrack0, 2\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack, \bigl\lbrack2, 0\bigr\rbrack\bigr\rbrack$

About

Examples	2
Checked against	Combinatorica 2 agree
Crosswalk	OEISCombinatorica

Implementation

mappedcombinatoricapackages/oracle/src/mappings.ts

Combinatorica's Compositions[n, k] allows zero parts: ours is WeakCompositions, not the strict IntegerCompositions.

See also: IntegerCompositions