汕头大学学报（自然科学版）

研究了在限定条件下的有序多子集组计数问题,推导了在条件:(A₁∪…∪A_p)∪(B₁∩…∩B_q)=N_n,A₁,…,A_p,B₁,…,B_q■N_n下,集函数x₁^|A_p|…x_p^|A_p|y₁^|B₁|…y_q^|B_q|的相关计数式,得到了一个重要的定理:W_n;p,q(x,y)=Σ_A1,…,A_p,B₁,…,B_q■N_n(A₁∪…∪A_p)∪(B₁∩…∩B_q)=N_nx₁^|A_p|…x_p^|A_p|y₁^|B₁|…y_q^|B_q|={[f(X)-1]g(Y)+y₁y₂…yq}ⁿ,其中f(X)=(1+x₁)(1+x₂)…(1+x_p),g(y)=(1+y₁)(1+y₂)…(1+y_q).并在此基础上,做了一系列推广及应用.

Counting problems on the ordered multi-subset group under the limited conditionsare studied. The counting formula of the set function"x₁^|A_p|…x_p^|A_p|y₁^|B₁|…y_q^|B_q|"under the conditions are derived:(A₁∪…∪A_p)∪(B₁∩…∩B_q)= N_n,A₁,…,A_p,B₁,…,B_q■N_n,and animportant theorem is obtained:W_n;p,q(x,y)=Σ_A1,…,A_p,B₁,…,B_q■N_n(A₁∪…∪A_p)∪(B₁∩…∩B_q)=N_nx₁^|A_p|…x_p^|A_p|y₁^|B₁|…y_q^|B_q|={[f(X)-1]g(Y)+y₁y₂…yq}ⁿAmong them,f(X)=(1+x₁)(1+x₂)…(1+x_p),g(y)=(1+y₁)(1+y₂)…(1+y_q)There are a series of promotion and application based on the theorem.