一组值的所有可能分组的数量? [英] Number of all possible groupings of a set of values?
问题描述
我想找到一个给定一定数量的整数的组合公式,我可以找到这些整数的所有可能组的数量(例如,所有的值都属于一个组)。
说我有3个整数,1,2,3
将会有5个分组:
1 2 3
1 | 2 | 3 |
1 2 | 3
1 | 2 3
2 | 1 3
我已经计算出这些计算N = 3到11,但我想在理论上表明。这些值是:(我相信它们是正确的)
$ $ p $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
5 52
6 203
7 877
8 4140
9 21147
10 115975
11 678570
这样做的原因是要查找完整图的分区总数。
任何建议或引用将不胜感激
您正在寻找的是 Set Partitons 。您正在寻找的计数是贝尔数字,请参阅wikipedia文章。
I want to find a combinatorial formula that given a certain number of integers, I can find the number of all possible groupings of these integers (such that all values belong to a single group)
Say I have 3 integers, 1, 2, 3 There would be 5 groupings:
1 2 3
1|2|3|
1 2|3
1|2 3
2|1 3
I have calculated these computationally for N = 3 to 11, but I am trying to theoretically assertain. These values are: (I believe they are correct)
num_integers num_groupings
3 5
4 15
5 52
6 203
7 877
8 4140
9 21147
10 115975
11 678570
The reason for doing this is to find the total number of partitionings of a complete graph.
Any advice, or references would be appreciated
What you are looking for is Set Partitons. The counts that you are looking for are Bell numbers, see the wikipedia article.
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