{"paper":{"title":"An infinite family of adsorption models and restricted Lukasiewicz paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Gary K Iliev, Richard Brak, Thomas Prellberg","submitted_at":"2011-05-02T12:12:46Z","abstract_excerpt":"We define $(k,\\ell)$-restricted Lukasiewicz paths, $k\\le\\ell\\in\\mathbb{N}_0$, and use these paths as models of polymer adsorption. We write down a polynomial expression satisfied by the generating function for arbitrary values of $(k,\\ell)$. The resulting polynomial is of degree $\\ell+1$ and hence cannot be solved explicitly for sufficiently large $\\ell$. We provide two different approaches to obtain the phase diagram. In addition to a more conventional analysis, we also develop a new mathematical characterization of the phase diagram in terms of the discriminant of the polynomial and a zero o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0306","kind":"arxiv","version":2},"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"}