Restricted set addition: The exceptional case of the Erdős–Heilbronn conjecture

Let A ≠ B be nonempty subsets of the group of integers modulo a prime p. If p ⩾ | A | + | B | − 2 , then at least | A | + | B | − 2 different residue classes can be represented as a + b , where a ∈ A , b ∈ B and a ≠ b . This result complements the solution of a problem of Erdős and Heilbronn obtained by Alon, Nathanson, and Ruzsa.