LLM aids discovery of new lower bounds for Shannon capacity of odd cycles

作者 PulseAugur 编辑部 · [1 个来源] · 2026-07-24 04:00

研究人员开发了新的方法来为奇数圈的香农容量建立改进的下界，特别是 C7、C11 和 C13。这些进展是通过在这些图的强幂中构建特定的独立集来实现的。值得注意的是，发现过程涉及与大型语言模型 (LLM) 的迭代交互，这凸显了 LLM 在生成复杂组合结构方面的日益增长的实用性。 AI

影响展示了 LLM 在辅助复杂组合数学研究方面的能力。

排序理由学术论文，详细介绍了新的数学界限和方法论。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.AI TIER_1 English(EN) · Nathaniel Itty, Christopher D. Rosin, Chase Carstensen, Daniel Reichman · 2026-07-24 04:00

奇偶循环香农容量的改进下界

arXiv:2607.21517v1 Announce Type: cross Abstract: The Shannon capacity $\Theta(G)$ of a graph $G$ quantifies the maximum rate at which information can be transmitted with zero error over a noisy channel. It is lower bounded by $\alpha(G^d)^{1/d}$ for any $d$, where $\alpha(G^d)$ …