Place n indistinguishable items into k distinguishable boxes

[castironpi at gmail.com]

On Feb 27, 8:40 pm, Michael Robertson <mcrobert... at hotmail.com> wrote:
> Hi,
>
> I need a generator which produces all ways to place n indistinguishable
> items into k distinguishable boxes.
>
> For n=4, k=3, there are (4+3-1)!/(3-1)!/4! = 15 ways.
>
> (0,0,4)
> (0,4,0)
> (4,0,0)
>
> (0,2,2)
> (2,0,2)
> (2,2,0)
>
> (0,1,3)
> (0,3,1)
> (3,0,1)
> (3,1,0)
>
> (1,1,2)
> (1,2,1)
> (2,1,1)
>
> The generator needs to be fast and efficient.
>
> Thanks.

Note that the boxes are indistinguishable, and as such, ( 1, 0, 3 ) ==
( 3, 0, 1 ), but != ( 3, 1, 0 ).  How so?