{"paper":{"title":"Regularity of powers of cover ideals of unimodular hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Nguyen Thu Hang, Tran Nam Trung","submitted_at":"2017-05-18T06:24:14Z","abstract_excerpt":"Let $\\H$ be a unimodular hypergraph over the vertex set $[n]$ and let $J(\\H)$ be the cover ideal of $\\H$ in the polynomial ring $R=K[x_1,\\ldots,x_n]$. We show that $\\reg J(\\H)^s$ is a linear function in $s$ for all $s\\geqslant r\\left\\lceil \\frac{n}{2}\\right\\rceil+1$ where $r$ is the rank of $\\H$. Moreover for every $i$, $a_i(R/J(\\H)^s)$ is also a linear function in $s$ for $s \\geqslant n^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06426","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"}