Is there a known algorithm to find all possible sets of positive integers such that the sum over each set equals an arbitrary integer, n?
Plainly, is there a known algorithm to find A:
$n\in N,A, B\subset N,B\in A, b\in B < n:$
$\forall B\in A:\sum_{b\in B} b=n$
?
I have searched for such an algorithm, but to no avail.
For example:
For $n=3:$ $A={{1,1,1],{1,2}}