To translate between the combinatorial and algebraic definitions, for i = 1 , … … , n − − 1 one may identify the Coxeter generator s i with the affine permutation that has window notation [ 1 , 2 , … … , i − − 1 , i + 1 , i , i + 2 , … … , n ] , and also identify the generator s 0 = s n with the affine permutation [ 0 , 2 , 3 , … … , n − − 2 , n − − 1 , n + 1 ] . More generally, every reflection (that is, a conjugate of one of the Coxeter generators) can be described uniquely as follows: for distinct integers i, j in { 1 , … … , n } and arbitrary integer k, it maps i to j − kn, maps j to i + kn, and fixes all inputs not congruent to i or j modulo n.