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Erdős-Heilbronn conjecture #36

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YaelDillies opened this issue Jan 22, 2025 · 0 comments
Open

Erdős-Heilbronn conjecture #36

YaelDillies opened this issue Jan 22, 2025 · 0 comments

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@YaelDillies
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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.

@YaelDillies YaelDillies converted this from a draft issue Jan 22, 2025
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