Package de.tilman_neumann.jml.combinatorics

Class FallingFactorial

java.lang.Object

de.tilman_neumann.jml.combinatorics.FallingFactorial

public class FallingFactorial
extends Object

Implementations of the falling factorial (n)_k = (n-k+1)*...*n. In combinatorics this can be interpreted as the number of variations of (n-k) and k indistinguishable objects of two different kinds. Note that the coefficients of the expanded polynomial are (signed) Stirling numbers of the first kind. E.g. (n)_5 = (n-4)*(n-3)*(n-2)*(n-1)*n = 24n - 50n^2 + 35n^3 - 10n^4 + n^5 = s(5,1)n + s(5,2)n^2 + s(5,3)n^3 + s(5,4)n^4 + s(5,5)n^5

Author:

Tilman Neumann

Constructor Summary

Constructors

Constructor	Description
FallingFactorial()

Method Summary

Modifier and Type	Method	Description
static BigInteger	fallingFactorial(int n, int k)	Computes the falling factorial.
static void	main(String[] args)	Test

Methods inherited from class java.lang.Object

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

Constructor Detail

FallingFactorial

public FallingFactorial()

Method Detail

fallingFactorial

public static BigInteger fallingFactorial(int n,
                                          int k)
                                   throws IllegalArgumentException

Computes the falling factorial.

Parameters:

n -

k -

Returns:

falling factorial (n)_k

Throws:

IllegalArgumentException - if k<0

main

public static void main(String[] args)

Test

Parameters:

args - ignored