# Multiset

A multiset is an 2-tulple (S, f), where $\displaystyle{ S }$ is a set and $\displaystyle{ f }$ is a frequency function (that returns the Frequency of a multiset member).

## References

### 2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/multiset Retrieved:2014-4-21.
• In mathematics, the notion of multiset (or bag) is a generalization of the notion of set in which members are allowed to appear more than once. For example, there is a unique set that contains the elements a and b and no others, but there are many multisets with this property, such as the multiset that contains two copies of a and one of b or the multiset that contains three copies of both a and b. The term "multiset" was coined by Nicolaas Govert de Bruijn in the 1970s. [1]

The use of multisets in mathematics and beyond predates the name "multiset" by many centuries: Knuth (1998) attributes the first study of multisets to the Indian mathematician Bhascara Acharya (circa 1150), who described permutations of multisets.

1. Knuth also lists other names that were proposed for multisets, such as list, bunch, bag, heap, sample, weighted set, collection, and suite.