徐利治、蒋茂森、朱自强在文献[1]中提出C(S^(m),)数,其枚举发生函数是(P.30～31)（1+t+t^2+…t^3）^(m)=sum from r=0 to ∞t^r[sum from h=0 to[r/s+1](-1)~k(_k^m)(m-1+r-k(S+1)/r-k(S+1))],其数C(S^m,r)=sum from h=0 to[r/s+1](-1)~k(_k^m)(m-1+r-k(S+1)/r-k(S+1))本文计论了C(S^m,r)数在“邮票排列问题”中的应用(文献[1],P32～33),得到下列公式B(S,n)=sum from (?) C((S-1)^(m-r),r)。本文讨论了C(S^m,r)数在概率论中的应用（文献[2],P12～13)。得到下列公式P(A)=C(S-1)^(m),λ-n)/s^(m)。
Generalization of inequality. Several imporatnt theorems are raised in this essay, such as: Theorem 4 suppose α_i,λ_(ij),μ_(ij),…,τ_(ij)(i=1,2,…,n;j=1,2,…,m)are all positive real numbers, such that ≥1. Then Theorem 5 Theorem 6 Suppose α_i>0,q_i>0(i=1,2,…,n)such that 0
