{"paper":{"title":"Toric ideals and diagonal 2-minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Anargyros Katsabekis","submitted_at":"2013-08-20T13:47:08Z","abstract_excerpt":"Let $G$ be a simple graph on the vertex set $\\{1,\\ldots,n\\}$ with $m$ edges. An algebraic object attached to $G$ is the ideal $P_{G}$ generated by diagonal 2-minors of an $n \\times n$ matrix of variables. In this paper we prove that if $G$ is bipartite, then every initial ideal of $P_{G}$ is generated by squarefree monomials of degree at most $\\left \\lfloor{\\frac{m+n+1}{2}} \\right \\rfloor$. Furthermore, we completely characterize all connected graphs $G$ for which $P_{G}$ is the toric ideal associated to a finite simple graph. Finally we compute in certain cases the universal Gr{\\\"o}bner basis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4308","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"}