容斥 反演

\[F_S=\sum_{T \subseteq S}G_T \]

\[G_S=\sum_{T \subseteq S}(-1)^{|S|-|T|}F_T \]

　

\[F_{S_1,S_2...S_n}=\sum_{T_1 \subseteq S_1,T_2 \subseteq S_2 ... T_n \subseteq S_n}G_{T_1,T_2...T_n} \]

\[G_{S_1,S_2...S_n}=\sum_{T_1 \subseteq S_1,T_2 \subseteq S_2 ... T_n \subseteq S_n}\prod_{i=1}^n (-1)^{|S_i|-|T_i|} F_{T_1,T_2...T_n} \]

　

\[F_i=\sum_{j=i}^nC_j^i G_j \]

\[G_i=\sum_{j=i}^n (-1)^{j-i} C_j^i F_j \]