Stirling (Apache Commons Numbers Combinatorics 1.2 API)

java.lang.Object
- org.apache.commons.numbers.combinatorics.Stirling

public final class Stirling
extends Object

Computation of Stirling numbers.

Since:: 1.2

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static long`	`stirlingS1(int n, int k)`	Returns the signed Stirling number of the first kind, "`s(n,k)`".
`static long`	`stirlingS2(int n, int k)`	Returns the Stirling number of the second kind, "`S(n,k)`", the number of ways of partitioning an `n`-element set into `k` non-empty subsets.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - stirlingS1
```
public static long stirlingS1(int n,
                              int k)
```
    Returns the signed Stirling number of the first kind, "s(n,k)". The number of permutations of n elements which contain exactly k permutation cycles is the nonnegative number: |s(n,k)| = (-1)^(n-k) s(n,k)
    
    Parameters:
    
    n - Size of the set
    
    k - Number of permutation cycles (0 <= k <= n)
    
    Returns:
    
    s(n,k)
    
    Throws:
    
    IllegalArgumentException - if n < 0, k < 0 or k > n.
    
    ArithmeticException - if some overflow happens, typically for n exceeding 20 (s(n,n-1) is handled specifically and does not overflow)
  - stirlingS2
```
public static long stirlingS2(int n,
                              int k)
```
    Returns the Stirling number of the second kind, "S(n,k)", the number of ways of partitioning an n-element set into k non-empty subsets.
    
    Parameters:
    
    n - Size of the set
    
    k - Number of non-empty subsets (0 <= k <= n)
    
    Returns:
    
    S(n,k)
    
    Throws:
    
    IllegalArgumentException - if n < 0, k < 0 or k > n.
    
    ArithmeticException - if some overflow happens, typically for n exceeding 25 and k between 20 and n-2 (S(n,n-1) is handled specifically and does not overflow)