For every affine permutation, and more generally every shift-equivariant bijection, the numbers u ( 1 ) , … … , u ( n ) must all be distinct modulo n. An affine permutation is uniquely determined by its window notation [ u ( 1 ) , … … , u ( n ) ] , because all other values of u can be found by shifting these values. Thus, affine permutations may also be identified with tuples [ u ( 1 ) , … … , u ( n ) ] of integers that contain one element from each congruence class modulo n and sum to 1 + 2 + ⋯ ⋯ + n .