{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:GEWWGZBKNXB3M4WOUAKDE34CSK","short_pith_number":"pith:GEWWGZBK","schema_version":"1.0","canonical_sha256":"312d63642a6dc3b672cea014326f8292aed4cd464f7f4b3cf4518cb0fc3d5b36","source":{"kind":"arxiv","id":"math/0107155","version":1},"attestation_state":"computed","paper":{"title":"Vanishing ideals of Lattice Diagram determinants","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"J.-C. Aval, N. Bergeron","submitted_at":"2001-07-21T00:08:41Z","abstract_excerpt":"A lattice diagram is a finite set $L=\\{(p_1,q_1),... ,(p_n,q_n)\\}$ of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is $\\Delta_L(\\X;\\Y)=\\det \\| x_i^{p_j}y_i^{q_j} \\|$. The space $M_L$ is the space spanned by all partial derivatives of $\\Delta_L(\\X;\\Y)$. We denote by $M_L^0$ the $Y$-free component of $M_L$. For $\\mu$ a partition of $n+1$, we denote by $\\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the Ferrers diagram of $\\mu$. Using homogeneous partially symmetric polynomials, we give here a dual description of the vanishing ideal of 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":"math/0107155","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2001-07-21T00:08:41Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d679a5c66a0beb832b65623dadca31bb868d30dd5976f989d16cc2125f712413","abstract_canon_sha256":"bb5f7314080510e93fc87b246687c42f2e087f07d0a5b7976e3cb30e095678c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:03.494328Z","signature_b64":"1SYlD8rz8SAUlhTxaf9rdCsYXiv8TTCoswhy5PxXc4bIPcI0v9fzKD6OkLxR1isr5I19x/uAH4tG238yECfxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"312d63642a6dc3b672cea014326f8292aed4cd464f7f4b3cf4518cb0fc3d5b36","last_reissued_at":"2026-05-18T01:00:03.493718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:03.493718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing ideals of Lattice Diagram determinants","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"J.-C. Aval, N. Bergeron","submitted_at":"2001-07-21T00:08:41Z","abstract_excerpt":"A lattice diagram is a finite set $L=\\{(p_1,q_1),... ,(p_n,q_n)\\}$ of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is $\\Delta_L(\\X;\\Y)=\\det \\| x_i^{p_j}y_i^{q_j} \\|$. The space $M_L$ is the space spanned by all partial derivatives of $\\Delta_L(\\X;\\Y)$. We denote by $M_L^0$ the $Y$-free component of $M_L$. For $\\mu$ a partition of $n+1$, we denote by $\\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the Ferrers diagram of $\\mu$. Using homogeneous partially symmetric polynomials, we give here a dual description of the vanishing ideal of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107155","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":"math/0107155","created_at":"2026-05-18T01:00:03.493831+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0107155v1","created_at":"2026-05-18T01:00:03.493831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107155","created_at":"2026-05-18T01:00:03.493831+00:00"},{"alias_kind":"pith_short_12","alias_value":"GEWWGZBKNXB3","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"GEWWGZBKNXB3M4WO","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"GEWWGZBK","created_at":"2026-05-18T12:25:50.254431+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/GEWWGZBKNXB3M4WOUAKDE34CSK","json":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK.json","graph_json":"https://pith.science/api/pith-number/GEWWGZBKNXB3M4WOUAKDE34CSK/graph.json","events_json":"https://pith.science/api/pith-number/GEWWGZBKNXB3M4WOUAKDE34CSK/events.json","paper":"https://pith.science/paper/GEWWGZBK"},"agent_actions":{"view_html":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK","download_json":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK.json","view_paper":"https://pith.science/paper/GEWWGZBK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0107155&json=true","fetch_graph":"https://pith.science/api/pith-number/GEWWGZBKNXB3M4WOUAKDE34CSK/graph.json","fetch_events":"https://pith.science/api/pith-number/GEWWGZBKNXB3M4WOUAKDE34CSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK/action/storage_attestation","attest_author":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK/action/author_attestation","sign_citation":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK/action/citation_signature","submit_replication":"https://pith.science/pith/GEWWGZBKNXB3M4WOUAKDE34CSK/action/replication_record"}},"created_at":"2026-05-18T01:00:03.493831+00:00","updated_at":"2026-05-18T01:00:03.493831+00:00"}