Cyclically Symmetric Entropy Inequalities

A cyclically symmetric entropy inequality is of the form $\hslash_{\mathcal{O}}\geq\bar{c}\hslash_{\mathcal{O}^{\prime}}$, where $\hslash_{\mathcal{O}}$ and $\hslash_{\mathcal{O}^{\prime}}$ are two cyclic orbit entropy terms. A computational approach is formulated for bounding the extremal value of $\bar{c}$, which is denoted by $\bar{c}_{\mathcal{O},\text{O}^{\prime}}$. For two non-empty orbits $\mathcal{O}$ and $\mathcal{O}^{\prime}$ of a cyclic group, it is said that $\mathcal{O}$ dominates $\mathcal{O}^{\prime}$ if $\bar{c}_{\mathcal{O},\mathcal{O}^{\prime}}=1$. Special attention is paid to characterizing such dominance relationship, and a graphical method is developed for that purpose.