{"paper":{"title":"The Number of Independent Sets in Hexagonal Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.IT","math.MP"],"primary_cat":"cs.IT","authors_text":"Jie Ding, Mohammad Noshad, Vahid Tarokh, Zhun Deng","submitted_at":"2015-05-26T16:29:50Z","abstract_excerpt":"A new method is proposed to derive rigorous bounds on {\\eta}, the growth rate of the logarithm of the number of independent sets on a hexagonal lattice. Specifically, we prove that 1.546440708536001 <= {\\eta} <= 1.5513, which improves upon the best known 1.5463 <= {\\eta} <= 1.5527 due to Nagy and Zeger. Our lower bound matches the numerical estimate of Baxter up to 9 digits after the decimal point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07038","kind":"arxiv","version":3},"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"}