stirling numbers of the second kind are used to determine how many ways an

*n*-set can be

partitioned into

*m* non-empty

subsets. it goes a little something like this..

m
0 1 2 3 4 5 6 7 8 9..
________________________________________________________________________
0| 1
1| 0 1
2| 0 1 1
3| 0 1 3 1
4| 0 1 7 6 1
n 5| 0 1 15 25 10 1
6| 0 1 31 90 65 15 1
7| 0 1 63 301 350 140 21 1
8| 0 1 127 966 1701 1050 266 28 1
9| 0 1 255 3025 7770 6951 2646 462 36 1
:|

these numbers are also sometimes represented in a

triangle, since half the chart is empty where

*m* >

*n*, that is, where the number of partitions is 0. how do you get these numbers (if, for example, you wanted to fill in row 10)? a

general rule for filling in the chart is S(

*n,m*) = (

*n*-1,

*m*-1) +

*m*(

*n*-1,

*m*).