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Stanley and Zanello showed that the average size of an $(s,s+1)$-core partition equals $\\binom{s+1}{3}/2$. Based on a bijection of Ford, Mai and Sze between self-conjugate $(s,t)$-core partitions and lattice paths in $\\lfloor \\frac{s}{2} \\rfloor\\times \\lfloor \\frac{t}{2}\\rfloor$ rectangle, we obtain the average size of a self-conjugate $(s,t)$-core partitio"},"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":"1405.2175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-09T08:57:07Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"63ef4c810f35f1d8999c05042dc1069c65382c22ec9be8bce15fcfc9edc49778","abstract_canon_sha256":"a351a16e512f598402a39b8fe658fcf395d254a1efcb8c86a88b9bad372791f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:13.469611Z","signature_b64":"eBSTyU3skeQYsev0JT1/Z7aEKsD5lVFS1SaIWfd4u8dG/dWWwyUb0xIk6m6zO7m4vxn0GcmuMcTGaMFmXKayAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfd1c3d27c66aa773a13dd7408086334fadf9077490203e7099aa895e23cb18e","last_reissued_at":"2026-05-18T02:52:13.468943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:13.468943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Average Size of a Self-conjugate (s, t)-Core Partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Harry H.Y. Huang, Larry X.W. Wang, William Y.C. Chen","submitted_at":"2014-05-09T08:57:07Z","abstract_excerpt":"Armstrong, Hanusa and Jones conjectured that if $s,t$ are coprime integers, then the average size of an $(s,t)$-core partition and the average size of a self-conjugate $(s,t)$-core partition are both equal to $\\frac{(s+t+1)(s-1)(t-1)}{24}$. Stanley and Zanello showed that the average size of an $(s,s+1)$-core partition equals $\\binom{s+1}{3}/2$. Based on a bijection of Ford, Mai and Sze between self-conjugate $(s,t)$-core partitions and lattice paths in $\\lfloor \\frac{s}{2} \\rfloor\\times \\lfloor \\frac{t}{2}\\rfloor$ rectangle, we obtain the average size of a self-conjugate $(s,t)$-core partitio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2175","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":"1405.2175","created_at":"2026-05-18T02:52:13.469042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.2175v1","created_at":"2026-05-18T02:52:13.469042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2175","created_at":"2026-05-18T02:52:13.469042+00:00"},{"alias_kind":"pith_short_12","alias_value":"X7I4HUT4M2VH","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"X7I4HUT4M2VHOOQT","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"X7I4HUT4","created_at":"2026-05-18T12:28:57.508820+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/X7I4HUT4M2VHOOQT3V2AQCDDGT","json":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT.json","graph_json":"https://pith.science/api/pith-number/X7I4HUT4M2VHOOQT3V2AQCDDGT/graph.json","events_json":"https://pith.science/api/pith-number/X7I4HUT4M2VHOOQT3V2AQCDDGT/events.json","paper":"https://pith.science/paper/X7I4HUT4"},"agent_actions":{"view_html":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT","download_json":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT.json","view_paper":"https://pith.science/paper/X7I4HUT4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.2175&json=true","fetch_graph":"https://pith.science/api/pith-number/X7I4HUT4M2VHOOQT3V2AQCDDGT/graph.json","fetch_events":"https://pith.science/api/pith-number/X7I4HUT4M2VHOOQT3V2AQCDDGT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT/action/storage_attestation","attest_author":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT/action/author_attestation","sign_citation":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT/action/citation_signature","submit_replication":"https://pith.science/pith/X7I4HUT4M2VHOOQT3V2AQCDDGT/action/replication_record"}},"created_at":"2026-05-18T02:52:13.469042+00:00","updated_at":"2026-05-18T02:52:13.469042+00:00"}