Let the number of partitions of n into parts each less than or equal to m be denoted P(n,m). Prove

P(n,m) = P(n, m-1) + P(n-m,m)

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- May 14th 2012, 04:14 PMBlinkyBooPartitions proof
Let the number of partitions of n into parts each less than or equal to m be denoted P(n,m). Prove

P(n,m) = P(n, m-1) + P(n-m,m) - May 14th 2012, 04:40 PMPlatoRe: Partitions proof
- May 14th 2012, 07:46 PMBlinkyBooRe: Partitions proof
what is mathcad? >.> ... i'm not really following that equation :(

I'm a little confused because there is a formula in the book about partitioning n into exactly r parts where order counts = C(n-1,r-1)

but then there's another one that says "the number of ways of writing n as the sum of r or fewer integers where the order of the summands matters is C(r+n-1,n)"

but i didn't think they applied because order shouldn't count, should it?

I was also trying to play with the concept that the number of partitions of n into r or less parts = the number of partitions of n into parts that are r or less, but have gotten nowhere so far :\

if m = 1 there should only be one partition, n itself, right?

and if m = n, then all the partitions = 1 - May 17th 2012, 09:10 PMBlinkyBooRe: Partitions proof
could you be more specific please?

- May 18th 2012, 03:37 AMPlatoRe: Partitions proof
You can study this web page.