Multiset

A multiset $𝑀$ is a generalization of a set which may contain the same element more than once, set where we write $s u p p 𝑀$ for the underlying set. This may be formalized as

as a set $s u p p 𝑀$ with a generalized characteristic function $𝜒 𝑀 : s u p p 𝑀 \to ℕ$ so that $𝜒 𝑀 (𝑠)$ is the multiplicity of $𝑠$ in $𝑀$
as a set $𝑀'$ with an equivalence relation $𝑅$ , such that $s u p p 𝑀 = 𝑀' / 𝑅$ and $𝜒 𝑀 ([𝑠]) = | [𝑠] |$ .

In these notes, we will write $M 𝑡$ for the multiset related to an ordered tuple $𝑡$ . When it is clear, I may use $𝑀$ to refer to $s u p p 𝑀$ .

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Multiset

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