number of the answers for the equation$$x_1+x_2+...+x_m=n$$$x_i$ , $m$ and $n$ are positive integers

Question

anonymous · Answer

i cant remember the formula...

anonymous · Answer

and n must be greater than m of course

experimentx · Answer

linear algebra?

anonymous · Answer

most likely combinations

experimentx · Answer

are x1, x2, ... xm variables?

anonymous · Answer

yes they are

asnaseer · Answer

I recall @KingGeorge mentioning something about this kind of problem a long time ago. I believe it relates to number theory - partitions - see here: http://en.wikipedia.org/wiki/Partition_%28number_theory%29

experimentx · Answer

oh ... partition!! I give up on this stuff.

anonymous · Answer

Thats it, Thanks...there is a neat formula for the problem..let me find it

asnaseer · Answer

yw - I am amazed that I even remembered this it was such a long time ago! :)

experimentx · Answer

couple of months ago i tried searching ... i don't think there is nice formula for it.
there is generating function and not so nice recurrence formula. I wonder if there is nice closed solution for it.

anonymous · Answer

see this plz

asnaseer · Answer

I also found this which may be of use: http://www.artofproblemsolving.com/Resources/Papers/LaurendiPartitions.pdf

experimentx · Answer

looks like stars and bars problem

experimentx · Answer

http://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

asnaseer · Answer

this also shows some formulas including a limiting case as n tends to infinity: http://dlmf.nist.gov/26.9

experimentx · Answer

lol .. this is stars and bars problem

anonymous · Answer

yes...thats exactly what i wanted...thanks guys

loser66 · Answer

it looks like this

experimentx · Answer

also the best way to visualize it is to put n |dw:1370464052718:dw|
the number of objects inside the bars are object inside category x_i

partition of integers seems similar .. only it doesn't work. it's a nightmare.