{:x 2, :y 2, :z 3} {2 2, 3 1}Multiplicity sets of {1 n} describe sets and multiplicity multisets of {n 1} describe additive partitions.

**Additive partitions:**

Additive partitions are partitions of the multiset {1 n}.

{1 4}, {1 2, 2 1}, {1 3}, {2 2}, {4 1}Every multiset that contains only a single element has partitions isomorphic to the additive partitions.

**Set partitions:**

Multisets whose multiplicities are all one can be described as sets:

{:x 1, :y 1, :z 1} #{#{:x} #{:y :z}}In Clojure, sets can be described using the pound sign # leaving out the multiplicity values of one.

**Multiplicative partitions:**

Every positive integer can be factored into a multiset of prime numbers. The multiplicities multiset of the prime factorization is known as the numbers prime signature.

(= (factors 24) {2 3, 3 1})Multiplicative partitions can be used to describe association structures in terms of the size of each place in the structure.

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