{"paper":{"title":"A canonical polytopal resolution for transversal monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Rahim Zaare-Nahandi","submitted_at":"2016-07-05T12:50:55Z","abstract_excerpt":"Let $S = k[x_{11}, \\cdots, x_{1b_1}, \\cdots, x_{n1}, \\cdots, x_{nb_n}]$ be a polynomial ring in $m = b_1 + \\cdots + b_n$ variables over a field $k$. For all $j$, $1\\le j \\le n$, let $P_j$ be the prime ideal generated by variables $\\{x_{j1}, \\cdots, x_{jb_j}\\}$ and let $$I_{n, t} = \\sum_{1\\le j_1< \\cdots <j_t\\le n} P_{j_1}\\ldots P_{j_t}$$ be the transversal monomial ideal of degree $t$ on $P_1, \\cdots, P_n$. We explicitly construct a canonical polytopal $\\mathbb{Z}^t$-graded minimal free resolution for the ideal $I_{n, t}$ by means of suitable gluing of polytopes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01228","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"}