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))