# Small Set Partitions

Small Set Partitions

This Demonstration shows the partitions of the set into blocks, where and are small. For example, you could split into the blocks , , and . This is written compactly as

.

{1,2,3,...,n}

k

n

k

{1,2,3,4,5}

{2}

{1,5}

{3,4}

2 |

15 |

34 |

The number of ways of partitioning a set of elements into nonempty subsets (or blocks) is the Stirling number of the second kind, . The total number of ways to partition a set into blocks is the Bell number =.

n

k

(k)

n

B

n

n

∑

k=1

(k)

n