Multiset multiplicity ( $c_{M} (x)$ )

The number of occurrences of

x

M

, always a nonnegative integer for ordinary finite multisets.

Table of contents
- Frequency count Multiset multiplicity
- Multiplicity function Multiset multiplicity

Frequency count

The number of times a value occurs in observed data. Keeping 26 indexed counters for lowercase alphabet characters gives constant-time frequency queries independent of document length.

Multiplicity function ( $c_{M} : T \to N_{0}$ )

The function mapping each possible element to its multiset multiplicity. Finite multisets correspond to nonnegative functions with finite support of a multiset. A functional representation can answer queries without supporting enumeration of all elements.

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