{"paper":{"title":"Entropy of hard square lattice gas with $k$ distinct species of particles: coloring problems and vertex models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Sahil Kumar Singh, Sudhir R. Jain","submitted_at":"2018-06-18T15:03:45Z","abstract_excerpt":"Coloring the faces of 2-dimensional square lattice with $k$ distinct colors such that no two adjacent faces have the same color is considered by establishing connection between the $k$ coloring problem and a generalized vertex model. Associating the colors with $k$ distinct species of particles with infinite repulsive force between nearest neighbors of the same type and zero chemical potential $\\mu$ associated with each species, the number of ways $[W(k)]^N$ for large $N$ is related to the entropy of the {\\it{hard square lattice gas}} at close packing of the lattice, where $N$ is the number of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06751","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"}