4 replies to this topic

[gammaman]

What does this formula mean and how do I use it?

S(n+1,m) = S(n,m-1)+m*S(n,m)

[Turk4n]

gammaman said:

What does this formula mean and how do I use it?

S(n+1,m) = S(n,m-1)+m*S(n,m)

What's
S=?
n=?
m=?
For care to explain that for me please :)

[gammaman]

The only other part I figured out is that S(n,m) = the total number of partitions on n elements with m blocks.

[PythonPower]

It appears to be a recurrence relation of some kind. The most important inference from this particular one would probably be:

S(n,m) = S(n-1,m-1)+m*S(n-1,m)
(I should note, you should watch what (n, m) this is correct for!)

You can probably work out some special cases (like maybe S(0, m) = ...) which allow you to use it in a kind of dynamic programming method.

[WingedPanther]

Adding to what PythonPower said,
It is an incomplete recurrence relation. You have to have the initial conditions. It is the mathematical equivalent of recursion in programming.