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 $2$.
翻译:改进Bohman和Holzman在2003年得到的结果,我们证明对于$n \geq 1$,$2n+1$循环补图的香农容量至少为$(2^{r_n} + 1)^{1/r_n} = 2 + \Omega(2^{-r_n}/r_n)$,其中$r_n = \exp(O((\log n)^2))$是将$2(n-1)$划分为2的幂的分割数。