{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7Y5GTRWFZ4Y2KSTKTPH7NW6M35","short_pith_number":"pith:7Y5GTRWF","schema_version":"1.0","canonical_sha256":"fe3a69c6c5cf31a54a6a9bcff6dbccdf64a345b01a54dc6d771ad4b6125ef736","source":{"kind":"arxiv","id":"1901.01591","version":2},"attestation_state":"computed","paper":{"title":"On enumerators of Smirnov words by descents and cyclic descents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brittney Ellzey, Michelle L. Wachs","submitted_at":"2019-01-06T18:42:59Z","abstract_excerpt":"A Smirnov word is a word over the positive integers in which adjacent letters must be different. A symmetric function enumerating these words by descent number arose in the work of Shareshian and the second named author on $q$-Eulerian polynomials, where a $t$-analog of a formula of Carlitz, Scoville, and Vaughan for enumerating Smirnov words is proved. A symmetric function enumerating a circular version of these words by cyclic descent number arose in the work of the first named author on chromatic quasisymmetric functions of directed graphs, where a $t$-analog of a formula of Stanley for enu"},"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":"1901.01591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-06T18:42:59Z","cross_cats_sorted":[],"title_canon_sha256":"25e626f9443a6a807dcfd7327966342ccb8cf03a019918f40aaa7e196162cc09","abstract_canon_sha256":"a30a078c369e073b20355984d206889de9b31f0d9486554be9f08b9dbcf0fed2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:43.911913Z","signature_b64":"jYLp4tFnEhyienEBxAzDis4O9sm0PIolTyXZ3sGj21jC16iLxgR/oRqj4M+r+NdSCeLGDRdVgqoYruyoSBuCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3a69c6c5cf31a54a6a9bcff6dbccdf64a345b01a54dc6d771ad4b6125ef736","last_reissued_at":"2026-05-17T23:47:43.911058Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:43.911058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On enumerators of Smirnov words by descents and cyclic descents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brittney Ellzey, Michelle L. Wachs","submitted_at":"2019-01-06T18:42:59Z","abstract_excerpt":"A Smirnov word is a word over the positive integers in which adjacent letters must be different. A symmetric function enumerating these words by descent number arose in the work of Shareshian and the second named author on $q$-Eulerian polynomials, where a $t$-analog of a formula of Carlitz, Scoville, and Vaughan for enumerating Smirnov words is proved. A symmetric function enumerating a circular version of these words by cyclic descent number arose in the work of the first named author on chromatic quasisymmetric functions of directed graphs, where a $t$-analog of a formula of Stanley for enu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01591","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":"1901.01591","created_at":"2026-05-17T23:47:43.911207+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01591v2","created_at":"2026-05-17T23:47:43.911207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01591","created_at":"2026-05-17T23:47:43.911207+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Y5GTRWFZ4Y2","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Y5GTRWFZ4Y2KSTK","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Y5GTRWF","created_at":"2026-05-18T12:33:12.712433+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/7Y5GTRWFZ4Y2KSTKTPH7NW6M35","json":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35.json","graph_json":"https://pith.science/api/pith-number/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/graph.json","events_json":"https://pith.science/api/pith-number/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/events.json","paper":"https://pith.science/paper/7Y5GTRWF"},"agent_actions":{"view_html":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35","download_json":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35.json","view_paper":"https://pith.science/paper/7Y5GTRWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01591&json=true","fetch_graph":"https://pith.science/api/pith-number/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/graph.json","fetch_events":"https://pith.science/api/pith-number/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/action/storage_attestation","attest_author":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/action/author_attestation","sign_citation":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/action/citation_signature","submit_replication":"https://pith.science/pith/7Y5GTRWFZ4Y2KSTKTPH7NW6M35/action/replication_record"}},"created_at":"2026-05-17T23:47:43.911207+00:00","updated_at":"2026-05-17T23:47:43.911207+00:00"}