Define $$A \hat + B = \{a + b \mid a \in A, b \in B, a \ne b\}$$ For $A$ an interval in $\mathbb Z$, $|A \hat + A| = 2|A| - 3$. The Erdős-Heilbronn conjecture says this is best possible. Let $A, B$ be sets in $\mathbb F_p$ such that $1 \le |A| < |B|$ and $|A| + |B| \le p + 2$. Then $$|A \hat + B| \ge |A| + |B| - 2$$ This is [Theorem 2.7 in the lecture notes](https://github.com/YaelDillies/maths-notes/blob/master/combinatorics.pdf).
