A multiset records a nonnegative integer multiplicity for each element of a set. A finite multiset has finite support and finite total multiplicity. Its cardinality is the sum of its multiplicities; its disjoint union with another multiset adds multiplicities. The hook lengths of a Young diagram form a multiset, since different cells can have equal lengths.
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A **multiset**, also known as a bag, is a generalization of a set that allows for multiple occurrences of the same element. In a standard set, each element can appear only once—meaning that sets are collections of distinct objects. In contrast, a multiset can contain the same element more than once, and each element is associated with a count representing its number of occurrences.