different between submultiset vs multiset

English

Etymology

sub- +? multiset

Noun

submultiset (plural submultisets)

1. A subset of a multiset.

Anagrams

• multisubset

English

Etymology

multi- +? set.

Noun

multiset (plural multisets)

1. (set theory) A generalized type of set in which multiple occurrences of an element are permitted.
   • 2002, Gheorghe P?un, 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}.

Synonyms

• (generalized type of set that may contain multiple occurrences of elements): bag, mset.

Hyponyms

• (generalized type of set that may contain multiple occurrences of elements): set

Related terms

• multisubset
• submultiset

Translations

See also

• multirelation