View source for Partitions

[[category:Math Functions]]
[[category:Analytica 5.0]]

''New to [[Analytica 5.0]]''

== Partitions(k, n) ==

Returns the number of different ways that «n» objects can be partitioned into «k» non-empty groups. This is called the [https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind Sterling number of the second kind].

== Examples ==

:<code>[[Partitions]]( 3, 5 )</code> &rarr; 25
The groupings would be:
#{a, b, c}, {d}, {e}
#{a, b, d}, {c}, {e}
#{a, b, e}, {c}, {d}
#{a, c, d}, {b}, {e}
#{a, c, e}, {b}, {d}
#{a, d, e}, {b}, {c}
#{b, c, d}, {a}, {e}
#{b, c, e}, {a}, {d}
#{b, d, e}, {a}, {c}
#{c, d, e}, {a}, {b}
#{a, b}, {c, d}, {e}
#{a, b}, (c}, {d, e}
#{a, b}, {c, e}, {d}
#{a, c}, {b, d}, {e}
#{a, c}, {b}, {d, e}
#{a, c}, {b, e}, {d}
#{a, d}, {b, c}, {e}
#{a, d}, {b}, {c, e}
#{a, d}, {c, e}, {d}
#{a, e}, {b, d}, {c}
#{a, e}, {b}, {d, c}
#{a, e}, {b, c}, {d}
#{b, c}, {a}, {d, e}
#{b, d}, {a}, {c, e}
#{b, e}, {a}, {c, d}

== See Also ==
* [[Combinations]]
* [[Permutations]]
* [[Factorial]]