{"paper":{"title":"Matroid toric ideals: complete intersection, minors and minimal systems of generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ignacio Garc\\'ia-Marco, Jorge Luis Ram\\'irez Alfons\\'in","submitted_at":"2014-08-02T21:07:20Z","abstract_excerpt":"In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $\\mathcal M$ such that its corresponding toric ideal $I_{\\mathcal M}$ is a complete intersection. Secondly, we handle with the problem of detecting minors of a matroid $\\mathcal M$ from a minimal set of binomial generators of $I_{\\mathcal M}$. In particular, given a minimal set of binomial generators of $I_{\\mathcal M}$ we provide a necessary condition for $\\mathcal M$ to have a minor isomorphic to $\\mathcal U_{d,2d}$ for $d \\geq 2$. This condition is proved to be suff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0419","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"}