One way of defining groups is by generators and relations. In this type of definition, generators are a subset of group elements that, when combined, produce all other elements. The relations of the definition are a system of equations that determine when two combinations of generators are equal. In this way, the affine symmetric group S ~ ~ n is generated by a set s 0 , s 1 , … … , s n − − 1 of n elements that satisfy the following relations: when n ≥ ≥ 3 ,