On the exterior algebra method applied to restricted set addition

In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of Erdős and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A of the p -element group Z / p Z (where p is a prime), at least min { p , m | A | − m 2 + 1 } different elements of the group can be written as the sum of m different elements of A . In this note we present an easily accessible simplified version of their proof for the case m = 2 , and explain how the method can be applied to obtain the corresponding inverse theorem.