{"paper":{"title":"Spatial mixing and the connective constant: Optimal bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"cs.DS","authors_text":"Alistair Sinclair, Daniel \\v{S}tefankovi\\v{c}, Piyush Srivastava, Yitong Yin","submitted_at":"2014-10-08T04:14:36Z","abstract_excerpt":"We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model (which is defined as a weighted sum over all matchings where each matching is given a weight $\\gamma^{|V| - 2 |M|}$ in terms of a fixed parameter gamma called the monomer activity) and the hard core model (which is defined as a weighted sum over all independent sets where an independent set I is given a weight $\\lambda^{|I|}$ in terms of a fixed parameter la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2595","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"}