Restricted sums of sets of cardinality $2p + 1$ in $\mathbb{Z}_p^2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910014408491008 |
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| author | Terkel, Jacinda |
| author_facet | Terkel, Jacinda |
| contents | Let $A\subseteq \mathbb{Z}_p^2$ be a set of size $2p+1$ for prime $p\geq 5$. In this paper, we prove that $A\hat{+}A=\{a_1+a_2\mid a_1,a_2\in A, a_1\neq a_2\}$ has cardinality at least $4p$. This result is the first advancement in over two decades on a variant of the Erdős-Heilbronn problem studied by Eliahou and Kervaire. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restricted sums of sets of cardinality $2p + 1$ in $\mathbb{Z}_p^2$ Terkel, Jacinda Combinatorics Number Theory 11B13 (Primary) 11P70 (Secondary) Let $A\subseteq \mathbb{Z}_p^2$ be a set of size $2p+1$ for prime $p\geq 5$. In this paper, we prove that $A\hat{+}A=\{a_1+a_2\mid a_1,a_2\in A, a_1\neq a_2\}$ has cardinality at least $4p$. This result is the first advancement in over two decades on a variant of the Erdős-Heilbronn problem studied by Eliahou and Kervaire. |
| title | Restricted sums of sets of cardinality $2p + 1$ in $\mathbb{Z}_p^2$ |
| topic | Combinatorics Number Theory 11B13 (Primary) 11P70 (Secondary) |
| url | https://arxiv.org/abs/2410.00143 |