{"paper":{"title":"New Lower Bounds for the Shannon Capacity of Odd Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"K. Ashik Mathew, Patric R. J. \\\"Osterg{\\aa}rd","submitted_at":"2015-04-07T05:12:43Z","abstract_excerpt":"The Shannon capacity of a graph $G$ is defined as $c(G)=\\sup_{d\\geq 1}(\\alpha(G^d))^{\\frac{1}{d}},$ where $\\alpha(G)$ is the independence number of $G$. The Shannon capacity of the cycle $C_5$ on $5$ vertices was determined by Lov\\'{a}sz in 1979, but the Shannon capacity of a cycle $C_p$ for general odd $p$ remains one of the most notorious open problems in information theory. By prescribing stabilizers for the independent sets in $C_p^d$ and using stochastic search methods, we show that $\\alpha(C_7^5)\\geq 350$, $\\alpha(C_{11}^4)\\geq 748$, $\\alpha(C_{13}^4)\\geq 1534$ and $\\alpha(C_{15}^3)\\geq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01472","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}