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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."},"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":"1607.01228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-07-05T12:50:55Z","cross_cats_sorted":[],"title_canon_sha256":"d285e9fd416232a95ee4a475ac6bbed6f83dddc4ac4b61a73c5ff3d9200fd17d","abstract_canon_sha256":"5d0dda654e3fe49dae8d737c9a637b40b49b946b17d8b5ed8955f9c79dcdf8ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:29.961559Z","signature_b64":"NgX79OwqN+k0JrPnsTCKn4CTKnzEvshe1obfQW9gEo5OlIu1SaM9UzPPeTI8hUhG74JyG9gdZKcFkwCi96h0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a518aa6e0f6a2d6893ed12a750d16a7845617ee626f89f70a2be148524fe3983","last_reissued_at":"2026-05-18T01:11:29.961213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:29.961213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.01228","created_at":"2026-05-18T01:11:29.961268+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01228v1","created_at":"2026-05-18T01:11:29.961268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01228","created_at":"2026-05-18T01:11:29.961268+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUMKU3QPNIWW","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUMKU3QPNIWWRE7N","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUMKU3QP","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB","json":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB.json","graph_json":"https://pith.science/api/pith-number/UUMKU3QPNIWWRE7NCKTVBULKPB/graph.json","events_json":"https://pith.science/api/pith-number/UUMKU3QPNIWWRE7NCKTVBULKPB/events.json","paper":"https://pith.science/paper/UUMKU3QP"},"agent_actions":{"view_html":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB","download_json":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB.json","view_paper":"https://pith.science/paper/UUMKU3QP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01228&json=true","fetch_graph":"https://pith.science/api/pith-number/UUMKU3QPNIWWRE7NCKTVBULKPB/graph.json","fetch_events":"https://pith.science/api/pith-number/UUMKU3QPNIWWRE7NCKTVBULKPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB/action/storage_attestation","attest_author":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB/action/author_attestation","sign_citation":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB/action/citation_signature","submit_replication":"https://pith.science/pith/UUMKU3QPNIWWRE7NCKTVBULKPB/action/replication_record"}},"created_at":"2026-05-18T01:11:29.961268+00:00","updated_at":"2026-05-18T01:11:29.961268+00:00"}