As RKGuy would say, "probably well known to those who know it", but I found this cute: There are two kinds of partitions in common use: (a) Partitions of integers. p(5) = 7 partitions of 5, which are: 5, 41, 32, 311, 221, 2111, 11111. There's a complicated formula for p(n). (b) Partitions of sets. The 5 partitions of the set {abc} are abc, ab/c, ac/b, a/bc, a/b/c. There's a different complicated formula for these. The objects being partitioned are important in case B, while only the sizes of the pieces matter in case A. The other day, I realized that these two concepts could be joined together, with partitions of bags (multisets, sets with repeated elements). Case A is the partitioning of a bag with only one kind of element, {x,x,x,x,x}, while case B is the partitioning of a bag with all elements distinct {a,b,c}. The first nontrivial bag that's in between cases A and B is {a,a,b}, whose partitions are aab, aa/b, ab/a, a/a/b. So {aaa} has 3 partitions, {aab} has 4, and {abc} has 5. Case A has some interesting generalizations (planar partitions, cubic partitions, etc.). I don't know of similar notions for case B, or for bags. The generating functions for case A and case B are (of course) different, but have some similarities. Perhaps there's an in-between generating function for bag partitions. Rich