An improved lower bound on the Shannon capacities of complements of odd cycles
<|reference_start|>An improved lower bound on the Shannon capacities of complements of odd cycles: Improving a 2003 result of Bohman and Holzman, we show that for $n \geq 1$, the Shannon capacity of the complement of the $2n+1$-cycle is at least $(2^{r_n} + 1)^{1/r_n} = 2 + \Omega(2^{-r_n}/r_n)$, where $r_n = \exp(O((\log n)^2))$ is the number of partitions of $2(n-1)$ into powers of $2$. We also discuss a connection between this result and work by Day and Johnson in the context of graph Ramsey numbers.<|reference_end|>
@article{zhu2024an,
    title={An improved lower bound on the Shannon capacities of complements of odd
  cycles},
    author={Daniel G. Zhu},
    journal={arXiv preprint arXiv:2402.10025},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.10025},
    primaryClass={math.CO cs.IT math.IT}
}