{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OOOUPUCV47QFEGU4YJYVI64WEL","short_pith_number":"pith:OOOUPUCV","schema_version":"1.0","canonical_sha256":"739d47d055e7e0521a9cc271547b9622e3258df5754c8904e1e6f59635284d40","source":{"kind":"arxiv","id":"1310.2930","version":1},"attestation_state":"computed","paper":{"title":"Schur-positivity in a Square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cristina Ballantine, Rosa Orellana","submitted_at":"2013-10-10T19:45:47Z","abstract_excerpt":"Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem. In this paper we study the Schur-positivity of a family of symmetric functions. Given a partition \\lambda, we denote by \\lambda^c its complement in a square partition (m^m). We conjecture a Schur-positivity criterion for symmetric functions of the form s_{\\mu'}s_{\\mu^c}-s_{\\lambda'}s_{\\lambda^c}, where \\lambda is a partition of weight |\\mu|-1 contained in \\mu and the complement of \\mu is taken in the same square partition as the complement of \\lambda. We prove the conjecture i"},"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":"1310.2930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-10T19:45:47Z","cross_cats_sorted":[],"title_canon_sha256":"4043601b3e14996029e7ed20464907f3f9338d0e6058d494606b9de9c59b80bf","abstract_canon_sha256":"f884a2af34bef379a796562b432fcaf8680430f6672d0fe48cbfc314ac3152ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:46.260715Z","signature_b64":"YO3ZPBU07Fm4ucvjTXKwILAxaw1RgDKsDxgiFuc8OFsqafv4qe9xPUPm3T/XDflH1EGrZDAFE4Pm+JtQrNXLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"739d47d055e7e0521a9cc271547b9622e3258df5754c8904e1e6f59635284d40","last_reissued_at":"2026-05-18T03:10:46.260114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:46.260114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schur-positivity in a Square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cristina Ballantine, Rosa Orellana","submitted_at":"2013-10-10T19:45:47Z","abstract_excerpt":"Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem. In this paper we study the Schur-positivity of a family of symmetric functions. Given a partition \\lambda, we denote by \\lambda^c its complement in a square partition (m^m). We conjecture a Schur-positivity criterion for symmetric functions of the form s_{\\mu'}s_{\\mu^c}-s_{\\lambda'}s_{\\lambda^c}, where \\lambda is a partition of weight |\\mu|-1 contained in \\mu and the complement of \\mu is taken in the same square partition as the complement of \\lambda. We prove the conjecture i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2930","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":"1310.2930","created_at":"2026-05-18T03:10:46.260231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2930v1","created_at":"2026-05-18T03:10:46.260231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2930","created_at":"2026-05-18T03:10:46.260231+00:00"},{"alias_kind":"pith_short_12","alias_value":"OOOUPUCV47QF","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OOOUPUCV47QFEGU4","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OOOUPUCV","created_at":"2026-05-18T12:27:54.935989+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/OOOUPUCV47QFEGU4YJYVI64WEL","json":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL.json","graph_json":"https://pith.science/api/pith-number/OOOUPUCV47QFEGU4YJYVI64WEL/graph.json","events_json":"https://pith.science/api/pith-number/OOOUPUCV47QFEGU4YJYVI64WEL/events.json","paper":"https://pith.science/paper/OOOUPUCV"},"agent_actions":{"view_html":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL","download_json":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL.json","view_paper":"https://pith.science/paper/OOOUPUCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2930&json=true","fetch_graph":"https://pith.science/api/pith-number/OOOUPUCV47QFEGU4YJYVI64WEL/graph.json","fetch_events":"https://pith.science/api/pith-number/OOOUPUCV47QFEGU4YJYVI64WEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL/action/storage_attestation","attest_author":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL/action/author_attestation","sign_citation":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL/action/citation_signature","submit_replication":"https://pith.science/pith/OOOUPUCV47QFEGU4YJYVI64WEL/action/replication_record"}},"created_at":"2026-05-18T03:10:46.260231+00:00","updated_at":"2026-05-18T03:10:46.260231+00:00"}