{"paper":{"title":"Bouquet algebra of toric ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Apostolos Thoma, Marius Vladoiu, Sonja Petrovi\\'c","submitted_at":"2015-07-09T23:21:23Z","abstract_excerpt":"To any toric ideal $I_A$, encoded by an integer matrix $A$, we associate a matroid structure called {\\em the bouquet graph} of $A$ and introduce another toric ideal called {\\em the bouquet ideal} of $A$. We show how these objects capture the essential combinatorial and algebraic information about $I_A$. Passing from the toric ideal to its bouquet ideal reveals a structure that allows us to classify several cases. For example, on the one end of the spectrum, there are ideals that we call {\\em stable}, for which bouquets capture the complexity of various generating sets as well as the minimal fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02740","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"}