Definition:Bell Number
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Definition
The Bell Numbers $B_n$ are a sequence of natural numbers defined as the number of ways a set with $n$ elements can be partitioned.
Sequence of Bell Numbers
The sequence of Bell numbers begins:
- $(1), 1, 2, 5, 15, 52, 203, 877, 4140, 21 \, 147, \ldots$
where the first $(1)$ is the zeroth Bell number $B_0$.
Examples
Example: $B_2$
From the definition of Bell number, $B_2$ is the number of ways a set with $2$ elements can be partitioned.
- $\set {a, b}$
- $\set {\set a, \set b}$
- $B_2 = 2$
Example: $B_3$
From the definition of Bell number, $B_3$ is the number of ways a set with $3$ elements can be partitioned.
- $\set {a, b, c}$
- $\set {\set a, \set {b, c} }$
- $\set {\set b, \set {a, c} }$
- $\set {\set c, \set {a, b} }$
- $\set {\set a, \set b, \set c}$
- $B_3 = 5$
Also see
- Results about Bell numbers can be found here.
Source of Name
This entry was named for Eric Temple Bell.