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

By PulseAugur Editorial · [1 sources] ·

Researchers have developed new methods to establish improved lower bounds for the Shannon capacity of odd cycles, specifically C7, C11, and C13. These advancements were achieved by constructing specific independent sets within the strong powers of these graphs. Notably, the discovery process involved iterative interactions with a Large Language Model (LLM), highlighting the growing utility of LLMs in generating complex combinatorial constructions. AI

IMPACT Demonstrates LLMs' capability in aiding complex combinatorial mathematics research.

RANK_REASON Academic paper detailing new mathematical bounds and methodology. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.AI →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

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

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  1. arXiv cs.AI TIER_1 English(EN) · Nathaniel Itty, Christopher D. Rosin, Chase Carstensen, Daniel Reichman ·

    Improved lower bounds for the Shannon capacity of odd cycles

    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 $\alpha(G^d)$ …

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