Comment #4 on issue 3501 by [email protected]: Missing partitions in sympy.utilities.iterables.multiset_partitions
http://code.google.com/p/sympy/issues/detail?id=3501
The relevant Knuth reference is Algorithm M, (Multipartitions in decreasing lexicographic order), page 429 of volume 4, TAOCP, section 7.2.1.5. While it is of course *possible* that there is an error in Knuth's presentation of the algorithm, that wouldn't be my first bet.
WRT the list of factorings in comment 3 -- yes, it looks like an improvement, although my feel for multiset partitions is not good enough that I can just eyeball it. It is still visiting the same factoring multiple times, but that is a known issue.
It looks like Sage implements multiset partitions (sage/combinat/subset.py). I'll see if I can use that to generate some test cases.
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