{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:S32YZELYATHDVXXI2YC2TYIOGW","short_pith_number":"pith:S32YZELY","schema_version":"1.0","canonical_sha256":"96f58c917804ce3adee8d605a9e10e359d1ee92e142f45cb0ac77cb95b43033e","source":{"kind":"arxiv","id":"2409.15982","version":2},"attestation_state":"computed","paper":{"title":"The ascent lattice on Dyck paths","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Luc Baril, Mehdi Naima, Mireille Bousquet-M\\'elou, Sergey Kirgizov","submitted_at":"2024-09-24T11:27:42Z","abstract_excerpt":"In the Stanley lattice defined on Dyck paths of size $n$, cover relations are obtained by replacing a valley $DU$ by a peak $UD$. We investigate a greedy version of this lattice, first introduced by Chenevi\\`ere, where cover relations replace a factor $DU^k D$ by $U^kD^2$. By relating this poset to another poset recently defined by Nadeau and Tewari, we prove that this still yields a lattice, which we call the ascent lattice, $L_n$. We then count intervals in $L_n$. Their generating function is found to be algebraic of degree $3$. The proof is based on a recursive decomposition of intervals in"},"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":"2409.15982","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-24T11:27:42Z","cross_cats_sorted":[],"title_canon_sha256":"6c35fb94b77fc984094ad0bf0e2f1a7bea2445010ec71d2d0797e35d991dc7e8","abstract_canon_sha256":"a6338722da2ac147d08eae7da0f7fc2060580f54502ce7ced06e032afb12743b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:32.227527Z","signature_b64":"BxC9LpMX//442d34AHcbdlxjh50wQ8pjtQRwwPhqEeUjnBm/JdfYCkAmP5+mpqsvUQvqSIRcYdRWo4WET5yyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96f58c917804ce3adee8d605a9e10e359d1ee92e142f45cb0ac77cb95b43033e","last_reissued_at":"2026-07-05T11:10:32.227026Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:32.227026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The ascent lattice on Dyck paths","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Luc Baril, Mehdi Naima, Mireille Bousquet-M\\'elou, Sergey Kirgizov","submitted_at":"2024-09-24T11:27:42Z","abstract_excerpt":"In the Stanley lattice defined on Dyck paths of size $n$, cover relations are obtained by replacing a valley $DU$ by a peak $UD$. We investigate a greedy version of this lattice, first introduced by Chenevi\\`ere, where cover relations replace a factor $DU^k D$ by $U^kD^2$. By relating this poset to another poset recently defined by Nadeau and Tewari, we prove that this still yields a lattice, which we call the ascent lattice, $L_n$. We then count intervals in $L_n$. Their generating function is found to be algebraic of degree $3$. The proof is based on a recursive decomposition of intervals in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.15982","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.15982/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2409.15982","created_at":"2026-07-05T11:10:32.227084+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.15982v2","created_at":"2026-07-05T11:10:32.227084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.15982","created_at":"2026-07-05T11:10:32.227084+00:00"},{"alias_kind":"pith_short_12","alias_value":"S32YZELYATHD","created_at":"2026-07-05T11:10:32.227084+00:00"},{"alias_kind":"pith_short_16","alias_value":"S32YZELYATHDVXXI","created_at":"2026-07-05T11:10:32.227084+00:00"},{"alias_kind":"pith_short_8","alias_value":"S32YZELY","created_at":"2026-07-05T11:10:32.227084+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.17628","citing_title":"Intervals in a family of Fibonacci lattices","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW","json":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW.json","graph_json":"https://pith.science/api/pith-number/S32YZELYATHDVXXI2YC2TYIOGW/graph.json","events_json":"https://pith.science/api/pith-number/S32YZELYATHDVXXI2YC2TYIOGW/events.json","paper":"https://pith.science/paper/S32YZELY"},"agent_actions":{"view_html":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW","download_json":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW.json","view_paper":"https://pith.science/paper/S32YZELY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.15982&json=true","fetch_graph":"https://pith.science/api/pith-number/S32YZELYATHDVXXI2YC2TYIOGW/graph.json","fetch_events":"https://pith.science/api/pith-number/S32YZELYATHDVXXI2YC2TYIOGW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW/action/storage_attestation","attest_author":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW/action/author_attestation","sign_citation":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW/action/citation_signature","submit_replication":"https://pith.science/pith/S32YZELYATHDVXXI2YC2TYIOGW/action/replication_record"}},"created_at":"2026-07-05T11:10:32.227084+00:00","updated_at":"2026-07-05T11:10:32.227084+00:00"}