multiset

English

Etymology

Coined by Nicolaas Govert de Bruijn, multi- +‎ set.

Noun

multiset (plural multisets)

1. (set theory) A generalized type of set in which multiple occurrences of an element are permitted.

   Synonyms: bag, mset

   Two words are anagrams if they are made up of the same multiset of letters.

   • 2002, Gheorghe Pǎun, Membrane Computing: An Introduction, Springer, page 49:

     Membrane computing essentially deals with multisets, which are sets with multiplicities associated with their elements.

   • 2006, Xin Chen, Lan Liu, Zheng Liu, Tao Jiang, On the Minimum Common Integer Partition Problem, Tiziana Calamoneri, Irene Finocchi, Giuseppe F. Italiano (editors), Algorithms and Complexity: 6th Italian Conference CIAC 2006, Proceedings, Springer, LNCS 3998, page 236,

     A partition of a positive integer n is a multiset of positive integers that add up to exactly n, and an integer partition of a multiset S of integers is defined as the multiset union of partitions of integers in S.

   • 2012, Edward A. Scheinerman, Mathematics: A Discrete Introduction Brooks/Cole (Cengage Learning), page 102,

     Two multisets are the same provided they contain the same elements with the same multiplicities. For example, {1, 2, 3, 3} = {3, 1, 3, 2}, but {1, 2, 3, 3} ≠ {1, 2, 3, 3, 3}.

Related terms

• multisubset
• submultiset

Translations

generalized type of set that may contain multiple occurrences of elements

• Chinese:

  Mandarin: 多重集 (duōchóngjí), 多重集合 (duōchóngjíhé)

• Czech: multimnožina f
• Finnish: monijoukko
• French: multiensemble (fr) m
• German: Multimenge f
• Italian: multiinsieme m
• Japanese: 多重集合 (たじゅうしゅうごう, tajūshūgō)
• Russian: мультимно́жество (ru) n (mulʹtimnóžestvo)
• Swedish: multimängd c

See also

• multigraph
• multirelation