Definition of "multiset"

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

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

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.

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

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}.

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