multiset
Sign in to saveIn mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist that contain only elements and , but vary in the multiplicities of their elements: The set contains only elements and , each having multiplicity 1 when is seen as a multiset. In the multiset , the element has multiplicity 2, and has multiplicity 1. In the multiset , and
Article
12 sectionsContents
- History
- Examples
- Definition
- Basic properties and operations
- Recurrence relation
- Generating series
- Generalization and connection to the negative binomial series
- Applications
- Generalizations
- See also
- Notes
- References
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist that contain only elements and , but vary in the multiplicities of their elements: The set contains only elements and , each having multiplicity 1 when is seen as a multiset. In the multiset , the element has multiplicity 2, and has multiplicity 1. In the multiset , and both have multiplicity 3.
These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, the order in which elements are listed does not matter in discriminating multisets, so and denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset can be denoted by .