Package de.tilman_neumann.jml.combinatorics

Class Stirling

java.lang.Object

de.tilman_neumann.jml.combinatorics.Stirling

public class Stirling
extends Object

Computation of Stirling numbers.

Author:

Tilman Neumann

Constructor Summary

Constructors

Constructor	Description
Stirling()

Method Summary

Modifier and Type	Method	Description
static BigInteger	absStirling1(int n, int k)	Absolute Stirling numbers of the first kind.
static void	main(String[] args)	Tests.
static BigInteger[]	nextStirling1Diag(BigInteger[] lastDiag, int n1, int k)
static BigInteger	rStirling1(int n, int k, int r)	Compute r-Stirling numbers of the first kind s(n,k,r)
static BigInteger	stirling1(int n, int k)	(Signed) Stirling numbers of the first kind.
static BigInteger[]	stirling1Diag(int n, int k)	Calculates the diagonal of Stirling numbers of the first kind S1(n-k+1,1), S1(n-k+2,2), ..., S1(n-1,k-1), S1(n,k).
static BigInteger	stirling2(int n, int k)	Stirling numbers of the second kind S(n,k).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Stirling

public Stirling()

Method Detail

stirling1

public static BigInteger stirling1(int n,
                                   int k)

(Signed) Stirling numbers of the first kind.

Parameters:

n - Upper parameter

k - Lower parameter

Returns:

s(n,k)

absStirling1

public static BigInteger absStirling1(int n,
                                      int k)

Absolute Stirling numbers of the first kind.

Parameters:

n - Upper parameter

k - Lower parameter

Returns:

|s(n,k)|

stirling2

public static BigInteger stirling2(int n,
                                   int k)

Stirling numbers of the second kind S(n,k).

Parameters:

n -

k -

Returns:

BigInt

See Also:

http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html

rStirling1

public static BigInteger rStirling1(int n,
                                    int k,
                                    int r)

Compute r-Stirling numbers of the first kind s(n,k,r)

Parameters:

n - Upper parameter

k - Lower parameter

r - r-value

Returns:

s(n,k,r)

stirling1Diag

public static BigInteger[] stirling1Diag(int n,
                                         int k)

Calculates the diagonal of Stirling numbers of the first kind S1(n-k+1,1), S1(n-k+2,2), ..., S1(n-1,k-1), S1(n,k).

Parameters:

n -

k -

Returns:

an array containing the Stirling numbers of the diagonal

nextStirling1Diag

public static BigInteger[] nextStirling1Diag(BigInteger[] lastDiag,
                                             int n1,
                                             int k)

main

public static void main(String[] args)

Tests.

Parameters:

args - ignored