Total Number of Set Partitions/Examples/4/Illustration
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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 $6.2$