C1+C2+··+Ck=n partition x1≥c2≥·≥xk≥1 composition c1+c2+·+ck=n xri≥1 partition composition x1,·,xk} (C1,·,Ck) permutation “on-to” @≥(（-1）k!pk(n) ⇥ ￾n ￾ 1 k ￾ 1 ⇥ partition composition partition permutation {x1, ··· , xk} ￾ (x1, ··· , xk) composition “on-to” ￾ x1 + x2 + ··· + xk = n xi ⇥ 1 x1 + x2 + ··· + xk = n x1 ￾ x2 ￾ ··· ￾ xk ￾ 1 ￾