partition{x1,·,ck} yi=xi+k-i x1≥C2≥··≥ck-2≥Ck-1≥Ck≥1 +k-1+k-2 +2 +1 y1>y2>···>yk-2>yk-1>yk>1 composition ofn) (y1,y2,,yk) permutation “1-1” n+-1 )<（ k-1partition {x1, ··· , xk} k!pk(n) ⇥ ￾n + k(k￾1) 2 ￾ 1 k ￾ 1 ⇥ +k ￾ 1 +k ￾ 2 +2 +1 x1 ⇥ x2 ⇥ ··· ⇥ xk￾2 ⇥ xk￾1 ⇥ xk ⇥ 1 y1 > y2 > ··· > yk￾2 > yk￾1 > yk > 1 yi = xi + k ￾ i “1-1” permutation ￾ (y1, y2,...,yk) composition of n + k(k￾1) 2