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).


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.