I know, it's a bit confusing. That's why I wrote:
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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.
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and:
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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.
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I'm sure there's standard terms for these, too, terms that I simply don't know.
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Ah, yes, thanks. Wikipedia writes:
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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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