{"paper":{"title":"Testing Equivalence to the Hamiltonian Cycle Polynomial","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Agrim Dewan (Indian Insitute of Science, Bengaluru)","submitted_at":"2026-06-25T06:31:46Z","abstract_excerpt":"The Hamiltonian Cycle polynomial, denoted as $HC_n$, is defined to be the sum of the weighted Hamiltonian Cycles in an $n$-vertex complete digraph, with vertices labeled $1$ to $n$ and edges weighted by formal variables $x_{i,j}$. Valiant (STOC 1979) studied the Permanent and $HC$, defined as the family $\\{HC_n | \\ n \\geq 1\\}$, and showed both families are VNP-complete, the former over any field of characteristic other than $2$, and the latter over any field. Since its introduction, $HC$ has been studied from the perspective of lower bounds by Jerrum-Snir (JACM 1982), determinantal complexity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26653","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26653/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}