The restricted sumsets in finite abelian groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910355199885312 |
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| author | Du, Shanshan Pan, Hao |
| author_facet | Du, Shanshan Pan, Hao |
| contents | Suppose that $k\geq 2$ and $A$ is a non-empty subset of a finite abelian group $G$ with $|G|>1$. Then the cardinality of the restricted sumset $$ k^\wedge A:=\{a_1+\cdots+a_k:\,a_1,\ldots,a_k\in A,\ a_i\neq a_j\text{ for }i\neq j\} $$ is at least $$ \min\{p(G), k|A|-k^2+1\}, $$ where $p(G)$ denotes the least prime divisor of $|G|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The restricted sumsets in finite abelian groups Du, Shanshan Pan, Hao Combinatorics Number Theory Suppose that $k\geq 2$ and $A$ is a non-empty subset of a finite abelian group $G$ with $|G|>1$. Then the cardinality of the restricted sumset $$ k^\wedge A:=\{a_1+\cdots+a_k:\,a_1,\ldots,a_k\in A,\ a_i\neq a_j\text{ for }i\neq j\} $$ is at least $$ \min\{p(G), k|A|-k^2+1\}, $$ where $p(G)$ denotes the least prime divisor of $|G|$. |
| title | The restricted sumsets in finite abelian groups |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2403.03549 |