7.1.27 Listing all compositions of an integer into k parts
A composition of a positive integer n is an ordered set of
non-negative integers which sum to n. For example, three
compositions of 4 are
These compositions have two, two and three elements, respectively.
The icomp command finds all
compositions of an integer with a given number of elements.
-
icomp accepts two mandatory arguments and one optional
argument:
-
n, a positive integer.
- k, a positive integer not larger than n.
- Optionally, either zeros=true (which is the default) or
zeros=false.
- icomp(n,k ⟨,zeros=bool ⟩)
returns the list of all compositions of n into k parts, where a part can be
0 if bool=true (the default),
or where each part is greater than 0 if bool=false.
Remark.
Using icomp with too large values of n can easily clutter your working memory
because the number of compositions rises exponentially.
Examples
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