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引用次数: 1
摘要
我们证明了如果$A$是一组素数阶$p$的子集，使得$|2A|<2.7652|A|$和$|A|<1.25\cdot10^{-6}p$，则$A$包含在一个等差数列中，其项最多为$|2A|- A|+1$，且$2A$包含一个等差数列，且项至少为$2|A|-1$。这改进了许多先前已知的结果，使其趋向于假设值$3| a |-4$，这样的语句应该成立。
We show that if $A$ is a subset of a group of prime order $p$ such that $|2A|<2.7652|A|$ and $|A|<1.25\cdot10^{-6}p$, then $A$ is contained in an arithmetic progression with at most $|2A|-|A|+1$ terms, and $2A$ contains an arithmetic progression with the same difference and at least $2|A|-1$ terms. This improves a number of previously known results towards the conjectured value $3|A|-4$ for which such an statement should hold..
期刊介绍：
The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.
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