AI 中文总结
该研究构造了不含k项等差数列的近连续序列，改进了此前Alon与Zaks1998年的相关界，还推广至带有界间隙序列的情形。
AI 中文摘要
若整数序列a₁,…,aₙ满足对1≤i≤n-1，a_{i+1}-a_i∈{1,2}，则称其为近连续序列。我们证明存在长度为Ω(2ᵏ/k²)的近连续序列不含k项等差数列，这改进了Alon与Zaks1998年的最佳已知界，还证明了带有界间隙序列的推广结论。
英文摘要
A sequence $a_1,\ldots,a_n$ of integers is nearly consecutive if $a_{i+1}-a_i \in \{1,2\}$ for $1 \leq i \leq n-1$. We prove that there are nearly consecutive sequences of length $Ω(2^k/k^2)$ that contain no $k$-term arithmetic progression. This improves on the previous best known bound of Alon and Zaks from 1998. We also prove a generalization for sequences with bounded gaps.
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