Set partitions generator

This online calculator generates all possible partitions of a given set.

Esta página existe graças aos esforços das seguintes pessoas:

Timur

Timur

Criado: 2019-12-23 11:37:33, Ultima atualização: 2021-02-24 12:00:45
Creative Commons Attribution/Share-Alike License 3.0 (Unported)

Este conteúdo é licenciado de acordo com a Licença Creative Commons de Atribuição/CompartilhaIgual 3.0 (Unported). Isso significa que você pode redistribuir ou modificar livremente este conteúdo sob as mesmas condições de licença e precisa atribuir ao autor original colocando um hyperlink para este trabalho no seu site. Além disto, favor não modificar qualquer referência ao trabalho original (caso houver) que estiverem contidas neste conteúdo.

This online calculator can generate all set partitions for a given set. A partition of a set is a grouping of the set's elements into non-empty subsets in such a way that every element is included in exactly one subset. Thus, the subsets' union is equal to the original set, and the intersection of any two subsets is the empty set.

Please note that the generation of all partitions is a combinatorial task, and a number of all possible partitions grows very rapidly with the size of a set. In fact, this number is pre-calculated and is knows as the Bell number. Thus, for a set of size 6, the Bell number is 203, and the Bell number for the set of size 12 is 4213597. For more Bell numbers, you can check out the Bell triangle calculator.

The algorithm is based on an enumeration algorithm for restricted growth strings aka restricted growth functions. For more information, check out Restricted Growth Strings Generator. Since partitions generation is done inside your browser, be cautious with big sets - you probably would not want to add more than 10 elements in a set unless you have a really good computer.

PLANETCALC, Set partitions generator

Set partitions generator

Set

Value
Items per page:

The file is very large. Browser slowdown may occur during loading and creation.

URL copiado para a área de transferência
PLANETCALC, Set partitions generator

Comentários