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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.05193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-06-05T16:05:45Z","cross_cats_sorted":[],"title_canon_sha256":"7dc0873c7b19e158cebcb4ff7a229c558497957cf7124048de10cca4dc6b063b","abstract_canon_sha256":"a497c007e507ae7b4db72abda080a39b7b5f23af7632643754befbf3937bcef2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:11.710778Z","signature_b64":"vnI7pzc0n/0/XAqPuIBTCCPE3pannjocj9AaRU826oBuUqKp6DzH+LhfwjbzFKACow/yU+loG0k762XCgoHFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5841e261b0e89ab1fdb84cab656582daace1225c395969ab48ffc5668260c110","last_reissued_at":"2026-07-03T01:17:11.710309Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:11.710309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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