{"paper":{"title":"Comparing invariants of toric ideals of bipartite graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Kieran Bhaskara","submitted_at":"2023-03-26T20:53:30Z","abstract_excerpt":"Let $G$ be a finite simple graph and let $I_G$ denote its associated toric ideal in the polynomial ring $R$. For each integer $n\\geq 2$, we completely determine all the possible values for the tuple $({\\rm reg}(R/I_G), {\\rm deg}(h_{R/I_G}(t)),{\\rm pdim}(R/I_G), {\\rm depth}(R/I_G),\\dim(R/I_G))$ when $G$ is a connected bipartite graph on $n$ vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.14818","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.14818/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"}