Multiset

A collection whose elements may occur multiple times, with a nonnegative integer multiplicity assigned to each element. Unlike a set, it records how many times each element occurs.

Multiplicity: The number of times an element occurs in a collection that allows repetition. Each element’s multiplicity is the defining data recorded by a multiset.
Multiset union: An operation combining multisets by taking the maximum multiplicity of each element. This union treats either collection’s occurrences as sufficient for membership.
Binomial coefficient: The number of ways to choose a fixed-size subset from a finite set. Counting multisets of fixed size leads to combinations with repetition.
Sequence: An ordered list of elements in which positions distinguish occurrences. A sequence preserves order, while a multiset records counts but ignores order.
Cardinality: The number of elements in a set or, when repetition counts, in a multiset. Multiset cardinality sums the multiplicities of all its elements.
Multiset sum: An operation combining multisets by adding the multiplicities of corresponding elements. Adding counts preserves every occurrence from both input multisets.
Stars and bars: A counting method for distributing indistinguishable objects among distinguishable boxes. Its solutions correspond to multisets with prescribed total size.
Set with repetition: An informal description of a collection that allows repeated elements, often used to mean multiset. The phrase is common but can obscure the distinction between sets and multisets.
Indicator function: A function that assigns one to members of a set and zero to nonmembers. A multiset generalizes membership indicators by allowing integer-valued counts.
Multiset intersection: An operation assigning each element the minimum of its multiplicities in two multisets. The minimum count captures occurrences shared by both collections.

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