Introducing supersymmetric frieze patterns and linear difference operators

We introduce a supersymmetric analog of the classical Coxeter frieze patterns. Our approach is based on the relation with linear difference operators. We define supersymmetric analogs of linear difference operators called Hills operators. The space of these superfriezes is an algebraic supervariety, which is isomorphic to the space of supersymmetric second order difference equations, called Hills equations.