Group Action configuration x [n][m] X (m]ln] permutation 不：回风 group G (πox)(i)=xr(π(i) group action o:GxX→X ·associativity:(π·o)ox=To(gox) ●identity:eox=rGroup Action 0 1 2 3 4 5 0 1 2 3 4 5 configuration x : [n] ! [m] permutation ⇡ : [n] 1-1 ￾￾￾! on-to [n] group action X = [m] [n] group G ￾ : G ⇥ X ! X • associativity: • identity: (⇡ · ￾) ￾ x = ⇡ ￾ (￾ ￾ x) e ￾ x = x (⇡ ￾ x)(i) = x(⇡(i))