Total Number of Set Partitions/Examples/4/Illustration

Example of Total Number of Set Partitions

Let a set $S$ of cardinality $4$ be exemplified by $S = \set {a, b, c, d}$.

Then the partitions of $S$ are:

$\set {a, b, c, d}$

$\set {\set a, \set {b, c, d} }$

$\set {\set b, \set {a, c, d} }$

$\set {\set c, \set {a, b, d} }$

$\set {\set d, \set {a, b, c} }$

$\set {\set {a, b}, \set {c, d} }$

$\set {\set {a, c}, \set {b, d} }$

$\set {\set {a, d}, \set {b, c} }$

$\set {\set a, \set b, \set {c, d} }$

$\set {\set a, \set c, \set {b, d} }$

$\set {\set a, \set d, \set {b, c} }$

$\set {\set b, \set c, \set {a, d} }$

$\set {\set b, \set d, \set {a, c} }$

$\set {\set c, \set d, \set {a, b} }$

$\set {\set a, \set b, \set c, \set d}$

Sources

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 6$. Indexed families; partitions; equivalence relations: Example $6.2$