{"paper":{"title":"Chromatic Polynomials for Families of Strip Graphs and their Asymptotic Limits","license":"","headline":"","cross_cats":["hep-lat","math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Martin Rocek, Robert Shrock, Shan-Ho Tsai (Institute for Theoretical Physics, State University of New York at Stony Brook)","submitted_at":"1997-12-13T19:00:54Z","abstract_excerpt":"We calculate the chromatic polynomials $P((G_s)_m,q)$ and, from these, the asymptotic limiting functions $W(\\{G_s\\},q)=\\lim_{n \\to \\infty}P(G_s,q)^{1/n}$ for families of $n$-vertex graphs $(G_s)_m$ comprised of $m$ repeated subgraphs $H$ adjoined to an initial graph $I$. These calculations of $W(\\{G_s\\},q)$ for infinitely long strips of varying widths yield important insights into properties of $W(\\Lambda,q)$ for two-dimensional lattices $\\Lambda$. In turn, these results connect with statistical mechanics, since $W(\\Lambda,q)$ is the ground state degeneracy of the $q$-state Potts model on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9712148","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"}