Package org.apache.commons.numbers.combinatorics

Class Stirling

java.lang.Object
org.apache.commons.numbers.combinatorics.Stirling
public final class Stirling extends Object
Computation of Stirling numbers.
Since:
1.2

  • Method Details

    • 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)