Multiset Partitions

A multiset is an orderless collection of elements in which elements may be repeated, as in . In this Demonstration, the elements of the multiset are arranged at the corners of a regular -gon. Elements in the same submultiset are connected with line segments (singletons appear as dots).

SNAPSHOTS

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DETAILS

Snapshot 1: when a multiset containing elements is a set—that is, no elements are repeated—the number of partitions is the Bell number, calculated with the Mathematica function BellB
Snapshot 2: at the other extreme is a multiset consisting of the same element repeated times, which has distinct partitions, where is the number of partitions of the integer , calculated with the Mathematica function PartitionsP
Snapshot 3: the general case has more than two elements with some element occurring more than once
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