{"paper":{"title":"On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hongmiao Yu","submitted_at":"2025-06-05T16:05:45Z","abstract_excerpt":"We study the weak and strong Lefschetz properties for $R/\\mathrm{in}(I_t)$, where $I_t$ is the ideal of a polynomial ring $R$ generated by the $t$-minors of an $m\\times n$ matrix of indeterminates, and $\\mathrm{in}(I_t)$ denotes the initial ideal of $I_t$ with respect to a diagonal monomial order. We show that when $I_t$ is generated by maximal minors (that is, $t=\\mathrm{min}\\{m,n\\}$), the ring $R/\\mathrm{in}(I_t)$ has the strong Lefschetz property for all $m$, $n$. In contrast, for $t<\\mathrm{min}\\{m,n\\}$, we provide a bound such that $R/\\mathrm{in}(I_t)$ fails to satisfy the weak Lefschetz "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05193","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05193/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}