Study On Representation Functions Of Subsets Of Finite Abel Groups

In this paper,we study two sets with the same representation functions on finite Abel group,and solve the following problems:Let G be a finite Abel group.Firstly,in the case of minimal symmetry difference,we determine A,B?G,such that for all x∈G,R_i(A,x)=R_i(B,x),i∈{1,2,3}.The second is solve the problem of all representation functions in the case of maximal symmetric difference.Moreover,this paper adopts two methods of combinatorial analysis and generating function,which is not only a natural extension of the representation function problems on Z_m,but also a generalization.