combinatorics / Zero-error information theory
Determine the Shannon capacities of odd cycles beyond $C_5$, or improve the best explicit bounds. Lovasz's theta function settled $C_5$ in 1979 and every longer odd cycle has stayed open since. The current records, all obtained with model assistance and formally verified, are $\Theta(C_7) \ge 3.258805369885$, $\Theta(C_{11}) \ge 5.294502522149$, $\Theta(C_{13}) \ge 6.302455083464$, $\Theta(C_{15}) \ge 7.301600534487$, $\Theta(C_{19}) \ge 9.357192705918$, $\Theta(C_{21}) \ge 10.342455853338$ and $\Theta(C_{23}) \ge 11.328224257774$.
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record lower bounds for seven odd cycles; the exact capacities remain open for every odd cycle beyond C5
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Determine the Shannon capacities of odd cycles beyond $C_5$, or improve the best explicit bounds. Lovasz's theta function settled $C_5$ in 1979 and every longer odd cycle has stayed open since. The current records, all obtained with model assistance and formally verified, are $\Theta(C_7) \ge 3.258805369885$, $\Theta(C_{11}) \ge 5.294502522149$, $\Theta(C_{13}) \ge 6.302455083464$, $\Theta(C_{15}) \ge 7.301600534487$, $\Theta(C_{19}) \ge 9.357192705918$, $\Theta(C_{21}) \ge 10.342455853338$ and $\Theta(C_{23}) \ge 11.328224257774$.
record lower bounds for seven odd cycles; the exact capacities remain open for every odd cycle beyond C5
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