"Stirling Number"

Introduction and distinction of two types of Stirling number (refer to csdn from Acdreamer)

Stirling number I ---s (n,k): A method that ranks n objects into a K non-empty loop arrangement (ring).

Recursive: S (n, k) = (n-1) *s (n-1, K) + S (n-1, k-1); 1<= K<n

Explanation: Consider the n+1 element 1, the formation of a circular arrangement alone, the remainder of the S (n-1, k-1) species method

2, and other elements together to form a circular arrangement, n-1 elements to form K loop arrangement method number is S (n-1,k), insert a total of n methods, a total of n*s (n-1,k) species

Boundary Condition: s (i, 0) = 0, i>=1
S (i, I) = 1, i>=0

Stirling number II ---S (n,k): total of n elements placed in K-sets ( number of methods to divide n individuals into K non-empty rooms without differences )

K! S (p,k): The number of methods to divide n individuals into k (e.g., rooms marked with a room number) (no vacancies).

Recursive: S (n, k) = K*s (n-1,k) +s (n-1,k-1), 1<= k<n
Boundary Condition: s (i, 0) = 0, i>=1
S (i, I) = 1, i>=0

Stirling number I and Stirling number II have the same initial conditions, but the recurrence relationship is different .

Expand

Bell Number---b[n]

B N is the number of partitioning methods for the set of cardinality n . A division of Set s is a family of 22 disjoint non-empty sets defined as s , and they are s.

Each bell number is the Stirling Number II.

"Stirling Number"