c1+c2+··+ck=n x1≥x2≥·≥xk≥1 Pk(n)=Pk-1(n-1)+pk(n-k) Case.I k=1 (x1,...,k-1)is a (k-1)-partition of n-1 Case.2 k 1 (c1-1,...,xk-1)is a k-partition of n-kCase.1 xk = 1 Case.2 xk > 1 (x1,...,xk￾1) (x1 ￾ 1,...,xk ￾ 1) is a k-partition of n ￾ k is a (k ￾ 1)-partition of n ￾ 1 pk(n) = pk￾1(n ￾ 1) + pk(n ￾ k) x1 + x2 + ··· + xk = n x1 ￾ x2 ￾ ··· ￾ xk ￾ 1 ￾