{"paper":{"title":"Generalized cover ideals and the persistence property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adam Van Tuyl, Ashwini Bhat, Jennifer Biermann","submitted_at":"2013-01-21T21:50:42Z","abstract_excerpt":"Let $I$ be a square-free monomial ideal in $R = k[x_1,\\ldots,x_n]$, and consider the sets of associated primes ${\\rm Ass}(I^s)$ for all integers $s \\geq 1$. Although it is known that the sets of associated primes of powers of $I$ eventually stabilize, there are few results about the power at which this stabilization occurs (known as the index of stability). We introduce a family of square-free monomial ideals that can be associated to a finite simple graph $G$ that generalizes the cover ideal construction. When $G$ is a tree, we explicitly determine ${\\rm Ass}(I^s)$ for all $s \\geq 1$. As cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5020","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":""},"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"}