I wrote:
>
> def pickk(k,N,m=0) :
> if k==1 :
> return ((n,) for n in range(m,N))
> else :
> return ((n,)+more for more in pickk(k-1,N,m+1)
> for n in range(m,more[0]))
>
> def partitionN(k,N) :
> subsets = [frozenset(S) for S in pickk(k,N)]
while it doesn't otherwise change results, changing this line to
subsets = [frozenset(S) for S in sorted(pickk(k,N))]
provides everything nicely ordered (e.g. lexicographically)
> def exhaust(rest,bound=0) :
> if len(rest) < k :
> if rest :
> yield [sorted(rest)]
> else :
> yield []
> for newbound in range(bound,len(subsets)) :
> S = subsets[newbound]
> if rest >= S :
> sS = [sorted(S)]
> for restpart in exhaust(rest-S,newbound+1) :
> yield sS+restpart
> return exhaust(set(range(N)))
>
> partition = lambda k,S : [[[S[j] for j in S0] for S0 in P0]
> for P0 in partitionN(k,len(S))]
>
> >>> partition(2,[1,2,3,4])
> [[[1, 2], [3, 4]], [[1, 3], [2, 4]], [[2, 3], [1, 4]]]
> >>> partition(3,[1,2,3,4])
> [[[1, 2, 3], [4]], [[1, 2, 4], [3]], [[1, 3, 4], [2]], [[2, 3, 4], [1]]]
>
>
> CAVEAT : insufficiently tested, not proved correct, uncommented,
> provided as is
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