Group Action configuration x:[n][m] X (m]linl permutation π：m1m group G on-to (πox)(i)=x(π() group action o:G×X→X ·associativity:（(π·o)ox=To(oox) ·identity::eor=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))