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 Sterling number of the second kind.

Examples

Partitions( 3, 5 ) → 25

The groupings would be:

1. {a, b, c}, {d}, {e}
2. {a, b, d}, {c}, {e}
3. {a, b, e}, {c}, {d}
4. {a, c, d}, {b}, {e}
5. {a, c, e}, {b}, {d}
6. {a, d, e}, {b}, {c}
7. {b, c, d}, {a}, {e}
8. {b, c, e}, {a}, {d}
9. {b, d, e}, {a}, {c}
10. {c, d, e}, {a}, {b}
11. {a, b}, {c, d}, {e}
12. {a, b}, (c}, {d, e}
13. {a, b}, {c, e}, {d}
14. {a, c}, {b, d}, {e}
15. {a, c}, {b}, {d, e}
16. {a, c}, {b, e}, {d}
17. {a, d}, {b, c}, {e}
18. {a, d}, {b}, {c, e}
19. {a, d}, {c, e}, {d}
20. {a, e}, {b, d}, {c}
21. {a, e}, {b}, {d, c}
22. {a, e}, {b, c}, {d}
23. {b, c}, {a}, {d, e}
24. {b, d}, {a}, {c, e}
25. {b, e}, {a}, {c, d}

See Also

• Combinations
• Permutations
• Factorial