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:


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


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


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


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


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


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