{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GH5IUMVN3FE4OMLHOWALK4D4S4","short_pith_number":"pith:GH5IUMVN","schema_version":"1.0","canonical_sha256":"31fa8a32add949c731677580b5707c97199df2c10719769ea7a162897cf51121","source":{"kind":"arxiv","id":"1709.07995","version":3},"attestation_state":"computed","paper":{"title":"Hall-Littlewood polynomials and a Hecke action on ordered set partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, Jia Huang, Travis Scrimshaw","submitted_at":"2017-09-23T03:34:50Z","abstract_excerpt":"We construct an action of the Hecke algebra $H_n(q)$ on a quotient of the polynomial ring $F[x_1, \\dots, x_n]$, where $F = \\mathbb{Q}(q)$. The dimension of our quotient ring is the number of $k$-block ordered set partitions of $\\{1, 2, \\dots, n \\}$. This gives a quantum analog of a construction of Haglund-Rhoades-Shimozono and interpolates between their result at $q = 1$ and work of Huang-Rhoades at $q = 0$."},"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":"1709.07995","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-23T03:34:50Z","cross_cats_sorted":[],"title_canon_sha256":"857abcc0fce27c4ac0a3ce726a09adc19edc56300a51b146f626c21a6868cdcd","abstract_canon_sha256":"2fadf0d403f481eacd3100e9d837fa3b41948ecbe3822eadf44bc2f849a81034"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:55.987851Z","signature_b64":"lE53TWegTYuEhdBIf3izC7/XzbvwRtuC0alAijVLFRe0b4mgD/uqLMTuXmaGZBNQ1viRXhBeqJa8i0sb7sFGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31fa8a32add949c731677580b5707c97199df2c10719769ea7a162897cf51121","last_reissued_at":"2026-05-17T23:52:55.987093Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:55.987093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hall-Littlewood polynomials and a Hecke action on ordered set partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, Jia Huang, Travis Scrimshaw","submitted_at":"2017-09-23T03:34:50Z","abstract_excerpt":"We construct an action of the Hecke algebra $H_n(q)$ on a quotient of the polynomial ring $F[x_1, \\dots, x_n]$, where $F = \\mathbb{Q}(q)$. The dimension of our quotient ring is the number of $k$-block ordered set partitions of $\\{1, 2, \\dots, n \\}$. This gives a quantum analog of a construction of Haglund-Rhoades-Shimozono and interpolates between their result at $q = 1$ and work of Huang-Rhoades at $q = 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07995","kind":"arxiv","version":3},"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":"1709.07995","created_at":"2026-05-17T23:52:55.987218+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.07995v3","created_at":"2026-05-17T23:52:55.987218+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07995","created_at":"2026-05-17T23:52:55.987218+00:00"},{"alias_kind":"pith_short_12","alias_value":"GH5IUMVN3FE4","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"GH5IUMVN3FE4OMLH","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"GH5IUMVN","created_at":"2026-05-18T12:31:15.632608+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/GH5IUMVN3FE4OMLHOWALK4D4S4","json":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4.json","graph_json":"https://pith.science/api/pith-number/GH5IUMVN3FE4OMLHOWALK4D4S4/graph.json","events_json":"https://pith.science/api/pith-number/GH5IUMVN3FE4OMLHOWALK4D4S4/events.json","paper":"https://pith.science/paper/GH5IUMVN"},"agent_actions":{"view_html":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4","download_json":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4.json","view_paper":"https://pith.science/paper/GH5IUMVN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.07995&json=true","fetch_graph":"https://pith.science/api/pith-number/GH5IUMVN3FE4OMLHOWALK4D4S4/graph.json","fetch_events":"https://pith.science/api/pith-number/GH5IUMVN3FE4OMLHOWALK4D4S4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4/action/storage_attestation","attest_author":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4/action/author_attestation","sign_citation":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4/action/citation_signature","submit_replication":"https://pith.science/pith/GH5IUMVN3FE4OMLHOWALK4D4S4/action/replication_record"}},"created_at":"2026-05-17T23:52:55.987218+00:00","updated_at":"2026-05-17T23:52:55.987218+00:00"}