{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OO7HEYBUJUOTTHYE4YW2N67WQQ","short_pith_number":"pith:OO7HEYBU","schema_version":"1.0","canonical_sha256":"73be7260344d1d399f04e62da6fbf6842bf598a122cb5c8d0e776ab5487a2479","source":{"kind":"arxiv","id":"1511.02804","version":2},"attestation_state":"computed","paper":{"title":"Difference operators for partitions under the Littlewood decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guo-Niu Han, Huan Xiong, Paul-Olivier Dehaye","submitted_at":"2015-11-09T19:11:14Z","abstract_excerpt":"The concept of $t$-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $t$-hooks. It is well-known that the hook lengths of multiples of $t$ can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes "},"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":"1511.02804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-09T19:11:14Z","cross_cats_sorted":[],"title_canon_sha256":"8e3d94d2e5ef8c46ffc60cc56f64b8c1f8475661bb59fed56d85b7bda5471e26","abstract_canon_sha256":"13e8b4fe8cdad030597337424fde6106a67361d4b9fc1877dad570a27fd3f290"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:28.577965Z","signature_b64":"6kapSDOy4BJws7IpUrqgjsuAwjWMoCSx8ZFHn6VMD4c2OVYPWfBCG+Wd/ile+rtvyOBBlM0OEuG/7RvRlTMtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73be7260344d1d399f04e62da6fbf6842bf598a122cb5c8d0e776ab5487a2479","last_reissued_at":"2026-05-18T00:48:28.577399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:28.577399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Difference operators for partitions under the Littlewood decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guo-Niu Han, Huan Xiong, Paul-Olivier Dehaye","submitted_at":"2015-11-09T19:11:14Z","abstract_excerpt":"The concept of $t$-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $t$-hooks. It is well-known that the hook lengths of multiples of $t$ can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02804","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":"1511.02804","created_at":"2026-05-18T00:48:28.577480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.02804v2","created_at":"2026-05-18T00:48:28.577480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02804","created_at":"2026-05-18T00:48:28.577480+00:00"},{"alias_kind":"pith_short_12","alias_value":"OO7HEYBUJUOT","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OO7HEYBUJUOTTHYE","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OO7HEYBU","created_at":"2026-05-18T12:29:34.919912+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/OO7HEYBUJUOTTHYE4YW2N67WQQ","json":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ.json","graph_json":"https://pith.science/api/pith-number/OO7HEYBUJUOTTHYE4YW2N67WQQ/graph.json","events_json":"https://pith.science/api/pith-number/OO7HEYBUJUOTTHYE4YW2N67WQQ/events.json","paper":"https://pith.science/paper/OO7HEYBU"},"agent_actions":{"view_html":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ","download_json":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ.json","view_paper":"https://pith.science/paper/OO7HEYBU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.02804&json=true","fetch_graph":"https://pith.science/api/pith-number/OO7HEYBUJUOTTHYE4YW2N67WQQ/graph.json","fetch_events":"https://pith.science/api/pith-number/OO7HEYBUJUOTTHYE4YW2N67WQQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ/action/storage_attestation","attest_author":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ/action/author_attestation","sign_citation":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ/action/citation_signature","submit_replication":"https://pith.science/pith/OO7HEYBUJUOTTHYE4YW2N67WQQ/action/replication_record"}},"created_at":"2026-05-18T00:48:28.577480+00:00","updated_at":"2026-05-18T00:48:28.577480+00:00"}