### Re^4: Faster alternative to Math::Combinatorics

by AppleFritter (Vicar)
 on Sep 01, 2017 at 17:01 UTC ( #1198536=note: print w/replies, xml ) Need Help??

I know, it's a bit confusing. That's why I wrote:

I'm trying to generate all multisets (bags) of a specific total "weight" (let's call it w), where each element comes from a given list (of numbers, in this case), and each list element may have multiplicity 0..w in each multiset.

and:

The order in which the multisets itself are generated isn't important to me either, BTW. I've only listed them in order for the sake of readability.

I'm sure there's standard terms for these, too, terms that I simply don't know.

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Re^5: Faster alternative to Math::Combinatorics
by Laurent_R (Canon) on Sep 01, 2017 at 17:40 UTC
If I understand you well, I think a selection of items from a set where the selection order is irrelevant is called a combination. See https://en.wikipedia.org/wiki/Combination. Note that combinations can be with or without repetitions.

Perhaps using this term might help you searching the Internet for algorithms.

Ah, yes, thanks. Wikipedia writes:

A k-combination with repetitions, or k-multicombination, or multisubset of size k from a set S is given by a sequence of k not necessarily distinct elements of S, where order is not taken into account: two sequences of which one can be obtained from the other by permuting the terms define the same multiset. In other words, the number of ways to sample k elements from a set of n elements allowing for duplicates (i.e., with replacement) but disregarding different orderings (e.g. {2,1,2} = {1,2,2}).

So it seems that they're called "multicombinations" or "multisubsets", and I wasn't too far off the mark when talking about multisets.

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