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Then $R/I^{\\rm Sp}_{(n-2,2)}$ is Gorenstein, and $R/I^{\\rm Sp}_{(d,d,1)}$ is a Cohen-Macaulay ring with a linear free resolution. In this paper, we construct minimal free resolutions of these rings. Berkesch Zamaere, Griffeth, and Sam had already studied minimal free resolutions of $R/I^{\\rm Sp}_{(n-d,d)}$, which are also Cohen-Macaulay, using heighly advanced technique of the representation the"},"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":"2010.06522","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-10-13T16:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"994480039183c7436ced57676a181545c07ef67a782af9cd4994676fbc99e19d","abstract_canon_sha256":"7ecc8a2d1eea83853a4df2367e1ec03778d064d2870efe4ab793a2e15ab51c38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:24:26.774973Z","signature_b64":"iyzNepQ/qKNd0URTy9nTKiuhkHcoqzRV8aqictfnYwN8aFHhqGp50RYPl5+qe7FIkBq+1XnOQB680KT/3lhzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"798cc2ec431a0749baf4cdd62a8536b740b5121f175cb17ff82346d35e30b6d2","last_reissued_at":"2026-07-05T03:24:26.774416Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:24:26.774416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elementary construction of minimal free resolutions of the Specht ideals of shapes $(n-2,2)$ and $(d,d,1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kohji Yanagawa, Kosuke Shibata","submitted_at":"2020-10-13T16:28:25Z","abstract_excerpt":"For a partition $\\lambda$ of $n \\in \\mathbb{N}$, let $I^{\\rm Sp}_\\lambda$ be the ideal of $R=K[x_1,\\ldots,x_n]$ generated by all Specht polynomials of shape $\\lambda$. 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