Restricted sums of sets of cardinality $2p + 1$ in $\mathbb{Z}_p^2$

Let $A \subseteq Z_{p}^{2}$ be a set of size $2 p + 1$ for prime $p \geq 5$ . In this paper, we prove that $A \hat{+} A = {a_{1} + a_{2} ∣ a_{1}, a_{2} \in A, a_{1} \neq a_{2}}$ has cardinality at least $4 p$ . This result is the first advancement in over two decades on a variant of the Erdős-Heilbronn problem studied by Eliahou and Kervaire.

Restricted sums of sets of cardinality $2 p + 1$ in $Z_{p}^{2}$

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Restricted sums of sets of cardinality $2 p + 1$ in $Z_{p}^{2}$

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Restricted sums of sets of cardinality 2p+12p+1 in Zp2Zp2​

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Restricted sums of sets of cardinality 2p+12p+1 in Zp2Zp2​

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Restricted sums of sets of cardinality $2 p + 1$ in $Z_{p}^{2}$

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Restricted sums of sets of cardinality $2 p + 1$ in $Z_{p}^{2}$

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