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Add Shannon 1956 upper bound plus reference #27

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14 changes: 8 additions & 6 deletions constants/9a.md
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Expand Up @@ -24,6 +24,7 @@ is the strong graph product.

| Bound | Reference | Comments |
| ----- | --------- | -------- |
| $7/2 = 3.5$ | [S1956] | Fractional clique cover bound |
| $\vartheta({\mathcal C}_{7}) \approx 3.3177$ | [L1979] | Lovász theta-function bound |

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## References

- [BMRRST1971] L. Baumert, R. McEliece, E. Rodemich, H. Rumsey, R. Stanley, H. Taylor. *A combinatorial packing
problem*. Computers in Algebra and Number Theory, American Mathematical Society, Providence,
- [S1956] C. Shannon. The zero error capacity of a noisy channel. IRE Transactions on Information Theory, vol. 2, no. 3 (1956), 8-19. doi: 10.1109/TIT.1956.1056798
- [BMRRST1971] L. Baumert, R. McEliece, E. Rodemich, H. Rumsey, R. Stanley, H. Taylor. A combinatorial packing
problem. Computers in Algebra and Number Theory, American Mathematical Society, Providence,
RI (1971), 97–108.
- [L1979] Lovász, L. *On the Shannon capacity of a graph*. IEEE Transactions on Information Theory **25** (1979), 1–7.
- [PS2018] Sven Polak, Alexander Schrijver. *New lower bound on the Shannon capacity of C7 from circular graphs*. Information Processing Letters, 143 (2019), 37-40. arXiv:1808.07438.
- [MO2017] K.A. Mathew, P.R.J. Östergård. *New lower bounds for the Shannon capacity of odd cycles*. Designs,
- [L1979] Lovász, L. On the Shannon capacity of a graph. IEEE Transactions on Information Theory **25** (1979), 1–7.
- [PS2018] Sven Polak, Alexander Schrijver. New lower bound on the Shannon capacity of $C_7$ from circular graphs. Information Processing Letters, 143 (2019), 37-40. arXiv:1808.07438.
- [MO2017] K.A. Mathew, P.R.J. Östergård. New lower bounds for the Shannon capacity of odd cycles. Designs,
Codes and Cryptography, 84 (2017), 13–22.
- [VZ2002] A. Vesel, J. Zerovnik, Improved lower bound on the Shannon capacity of $C_7$, Information Processing
- [VZ2002] A. Vesel, J. Zerovnik. Improved lower bound on the Shannon capacity of $C_7$. Information Processing
Letters, 81 (2002), 277–282.

## Contribution notes
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