From 0837c8c18a23ed3d2d3bf8779ecad7f2c6f5060b Mon Sep 17 00:00:00 2001 From: Jeroen Zuiddam Date: Sun, 1 Feb 2026 13:17:10 +0100 Subject: [PATCH] Add Shannon 1956 upper bound plus reference --- constants/9a.md | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/constants/9a.md b/constants/9a.md index d2ad8aa..c8adff1 100644 --- a/constants/9a.md +++ b/constants/9a.md @@ -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 | --- @@ -51,14 +52,15 @@ channel whose confusability graph is $G$. ## 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