{"paper":{"title":"In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Erin Bela, Giuseppe Favacchio, Nghia Tran","submitted_at":"2018-09-24T08:23:48Z","abstract_excerpt":"The aim of this paper is to study the associated primes of powers of squarefree monomial ideals. Hypergraphs and squarefree monomial ideals are strongly connected. The cover ideal $J(H)$ of a hypergraph $H$ is the intersection of the primes corresponding to the edges of $H$. We define the $shadow$ of $H$ as a certain set of smaller hypergraphs related to $H$. We then describe how the shadows of $H$ preserve information about the associated primes of the powers of $J(H)$. Some implications to the persistence property are studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08796","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":""},"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"}