{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:P35B6622WBV3V2JWVW4EIEAOPA","short_pith_number":"pith:P35B6622","schema_version":"1.0","canonical_sha256":"7efa1f7b5ab06bbae936adb844100e783e46a235c98cb8cbc605c2c0909abdc8","source":{"kind":"arxiv","id":"1702.05634","version":2},"attestation_state":"computed","paper":{"title":"Explicit expressions for the moments of the size of an (n, dn-1)-core partition with distinct parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Zaleski","submitted_at":"2017-02-18T17:19:52Z","abstract_excerpt":"In a previous paper (arXiv:1608.02262), we used computer-assisted methods to find explicit expressions for the moments of the size of a uniform random (n,n+1)-core partition with distinct parts. In particular, we conjectured that the distribution is asymptotically normal. However, our analysis hinged on a characterization of (n,n+1)-core partitions given by Straub, which is not readily generalized to other families of simultaneous core partitions.\n  In another paper (arXiv:1611.05775) with Doron Zeilberger, we made use of the characterization in terms of posets to analyze (2n+1,2n+3)-core part"},"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":"1702.05634","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-18T17:19:52Z","cross_cats_sorted":[],"title_canon_sha256":"89c35edb82fd3345d864e6b2f80c5549e77ca25acdc1447e0478067b9d21a485","abstract_canon_sha256":"617f258bb2642d9a43118e9008aa04edfb7cf408c5ec9e17f048564127be9718"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:51.002307Z","signature_b64":"JRHps9Ut461uHuGw5LUaXKm5jmc6YaZIyQd6Bn1I3fTZnrUv2ecjcJvCHr53WFRE4yd4anuMjXxUFEWdt+00BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7efa1f7b5ab06bbae936adb844100e783e46a235c98cb8cbc605c2c0909abdc8","last_reissued_at":"2026-05-18T00:32:51.001671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:51.001671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit expressions for the moments of the size of an (n, dn-1)-core partition with distinct parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Zaleski","submitted_at":"2017-02-18T17:19:52Z","abstract_excerpt":"In a previous paper (arXiv:1608.02262), we used computer-assisted methods to find explicit expressions for the moments of the size of a uniform random (n,n+1)-core partition with distinct parts. In particular, we conjectured that the distribution is asymptotically normal. However, our analysis hinged on a characterization of (n,n+1)-core partitions given by Straub, which is not readily generalized to other families of simultaneous core partitions.\n  In another paper (arXiv:1611.05775) with Doron Zeilberger, we made use of the characterization in terms of posets to analyze (2n+1,2n+3)-core part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05634","kind":"arxiv","version":2},"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":"1702.05634","created_at":"2026-05-18T00:32:51.001766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.05634v2","created_at":"2026-05-18T00:32:51.001766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05634","created_at":"2026-05-18T00:32:51.001766+00:00"},{"alias_kind":"pith_short_12","alias_value":"P35B6622WBV3","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"P35B6622WBV3V2JW","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"P35B6622","created_at":"2026-05-18T12:31:37.085036+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/P35B6622WBV3V2JWVW4EIEAOPA","json":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA.json","graph_json":"https://pith.science/api/pith-number/P35B6622WBV3V2JWVW4EIEAOPA/graph.json","events_json":"https://pith.science/api/pith-number/P35B6622WBV3V2JWVW4EIEAOPA/events.json","paper":"https://pith.science/paper/P35B6622"},"agent_actions":{"view_html":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA","download_json":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA.json","view_paper":"https://pith.science/paper/P35B6622","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.05634&json=true","fetch_graph":"https://pith.science/api/pith-number/P35B6622WBV3V2JWVW4EIEAOPA/graph.json","fetch_events":"https://pith.science/api/pith-number/P35B6622WBV3V2JWVW4EIEAOPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA/action/storage_attestation","attest_author":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA/action/author_attestation","sign_citation":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA/action/citation_signature","submit_replication":"https://pith.science/pith/P35B6622WBV3V2JWVW4EIEAOPA/action/replication_record"}},"created_at":"2026-05-18T00:32:51.001766+00:00","updated_at":"2026-05-18T00:32:51.001766+00:00"}