发表机构
Northwestern Polytechnical University（西北工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过计算机辅助证明，在对称Kløve-Mossige类中，每个固定传感器数量下的最大化传感器集均为Kløve数组，从而将优化问题简化为Kløve参数搜索。
AI 中文摘要
Rajamäki和Koivunen提出了一个问题：在具有连续和共阵列的最小冗余对称Kløve-Mossige数组中，是否总是Kløve数组。我们给出了一个计算机辅助证明，表明在每一个固定的传感器数量下，每个最大化传感器集都属于Kløve类。该论证对生成器与其移位反射之间的重叠进行了分类，然后界定了Kløve类之外的假设优化器的孔径。将这些界限与经典的Kløve构造进行比较，解决了所有至少330个传感器数量的情况。一个精确的整数证书覆盖了从2到329的剩余数量，并将每个等式情况与一个Kløve数组作为完整集合相匹配。因此，在完整对称Kløve-Mossige类中的优化简化为先前已知的对Kløve参数的搜索。该定理涉及这一特定类，而非无限制稀疏数组或所有受限加法基。
英文摘要
Rajam$\unicode{228}$ki and Koivunen asked whether minimum-redundancy symmetric Kl$\unicode{248}$ve-Mossige arrays with contiguous sum co-arrays are always Kl$\unicode{248}$ve arrays. We give a computer-assisted proof that, at every fixed sensor count, every maximizing sensor set belongs to the Kl$\unicode{248}$ve class. The argument classifies the overlaps between a generator and its shifted reflection, then bounds the aperture of a hypothetical optimizer outside the Kl$\unicode{248}$ve class. Comparing these bounds with a classical Kl$\unicode{248}$ve construction settles all sensor counts at least 330. An exact integer certificate covers the remaining counts from 2 through 329 and matches every equality case to a Kl$\unicode{248}$ve array as a complete set. Consequently, optimization within the full symmetric Kl$\unicode{248}$ve-Mossige class reduces to the previously known search over Kl$\unicode{248}$ve parameters. The theorem concerns this specified class, rather than unrestricted sparse arrays or all restricted additive bases.
Comments14 pages, 1 figure, 1 table. Verification code and certificates included as ancillary files. Code repository: https://github.com/Yan-ll9/kloeve-optimality
