[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
]