A multiset, also called a bag or mset, modifies the concept of a set by allowing multiple instances of each of its elements, with the number of instances of a given element called its multiplicity. The set {a, b} and the multisets {a, a, b} and {a, a, a, b, b, b} are all different as multisets, since they assign different multiplicities to a and b, even though they share the same underlying elements. As with ordinary sets, and unlike tuples, the order in which elements are listed does not matter, so {a, a, b} and {a, b, a} denote the same multiset. The cardinality of a multiset is the sum of the multiplicities of all its elements; Nicolaas Govert de Bruijn coined the word multiset in the 1970s.
Facts
Origin YearDates the 1675 publication by Jean Prestet of a general rule for multiset permutations, the earliest precisely dated formal mathematical treatment named in the source; an earlier circa 1150 study by Bhaskaracharya is dated only approximately, and the word multiset itself was coined later still, by Nicolaas Govert de Bruijn in the 1970s. Connections
Associated With
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Source Multiset (Wikipedia)
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Sources
1. Multiset (Wikipedia)
Wikimedia FoundationLead section
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.
History section
Jean Prestet published a general rule for multiset permutations in 1675.
Lead sentence
a multiset (or bag, or mset) is a modification of the concept of a set
Attributed To: Nicolaas Govert de Bruijn, Lead
Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth.
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