Question

Let P(r,k) denote the number of partitions of r into exactly k parts.

a. Show that P(r,k) = P(r-1, k-1) + P(r-k,k)

any hint how to prove it?

Answer 1

b. \(\sum_{j=1}^{k} P \left( r-k,j \right) = P \left( r,k \right)\)