{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:5L6ATRKVSSATYWYNTGRAMRDWCJ","short_pith_number":"pith:5L6ATRKV","schema_version":"1.0","canonical_sha256":"eafc09c55594813c5b0d99a20644761270ef6f0cea2a5025fba2971ed24e9fa1","source":{"kind":"arxiv","id":"2302.12425","version":2},"attestation_state":"computed","paper":{"title":"Bender-Knuth involutions on linear extensions of posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Anh Trong Nam Hoang, Benjamin Przybocki, Janabel Xia, Judy Hsin-Hui Chiang, Matthew Kendall, Ryan Lynch, Son Nguyen","submitted_at":"2023-02-24T03:11:40Z","abstract_excerpt":"We study the permutation group $\\mathcal{BK}_P$ generated by Bender-Knuth moves on linear extensions of a poset $P$, an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets $P$ for which the cactus relations hold in $\\mathcal{BK}_P$. We also examine $\\mathcal{BK}_P$ as a subgroup of the symmetric group $\\mathfrak{S}_{\\mathcal{L}(P)}$ on the set of linear extensions of $P$ with the focus on analyzing posets $P$ for which $\\mathcal{BK}_P = \\mathfrak{S}_{\\mathcal{L}(P)}$."},"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":"2302.12425","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-24T03:11:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"98b71abc7da7d6d743d93944a85f57f18ee29e5e7b033c94efaf347abca200f3","abstract_canon_sha256":"cb2595774788957ce5320339550259e10c12246d0e2fedd12cce334b0722614a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:59:49.147260Z","signature_b64":"pzMYLKTA9npoH6QEmOLdVUbAkr5d1UgT1/K5cacGO6PdChk7216QF/nvc+59325LfsMZMJn7TOK7V2/NfPUTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eafc09c55594813c5b0d99a20644761270ef6f0cea2a5025fba2971ed24e9fa1","last_reissued_at":"2026-07-05T07:59:49.146645Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:59:49.146645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bender-Knuth involutions on linear extensions of posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Anh Trong Nam Hoang, Benjamin Przybocki, Janabel Xia, Judy Hsin-Hui Chiang, Matthew Kendall, Ryan Lynch, Son Nguyen","submitted_at":"2023-02-24T03:11:40Z","abstract_excerpt":"We study the permutation group $\\mathcal{BK}_P$ generated by Bender-Knuth moves on linear extensions of a poset $P$, an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets $P$ for which the cactus relations hold in $\\mathcal{BK}_P$. We also examine $\\mathcal{BK}_P$ as a subgroup of the symmetric group $\\mathfrak{S}_{\\mathcal{L}(P)}$ on the set of linear extensions of $P$ with the focus on analyzing posets $P$ for which $\\mathcal{BK}_P = \\mathfrak{S}_{\\mathcal{L}(P)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.12425","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/2302.12425/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":"2302.12425","created_at":"2026-07-05T07:59:49.146721+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.12425v2","created_at":"2026-07-05T07:59:49.146721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.12425","created_at":"2026-07-05T07:59:49.146721+00:00"},{"alias_kind":"pith_short_12","alias_value":"5L6ATRKVSSAT","created_at":"2026-07-05T07:59:49.146721+00:00"},{"alias_kind":"pith_short_16","alias_value":"5L6ATRKVSSATYWYN","created_at":"2026-07-05T07:59:49.146721+00:00"},{"alias_kind":"pith_short_8","alias_value":"5L6ATRKV","created_at":"2026-07-05T07:59:49.146721+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/5L6ATRKVSSATYWYNTGRAMRDWCJ","json":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ.json","graph_json":"https://pith.science/api/pith-number/5L6ATRKVSSATYWYNTGRAMRDWCJ/graph.json","events_json":"https://pith.science/api/pith-number/5L6ATRKVSSATYWYNTGRAMRDWCJ/events.json","paper":"https://pith.science/paper/5L6ATRKV"},"agent_actions":{"view_html":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ","download_json":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ.json","view_paper":"https://pith.science/paper/5L6ATRKV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.12425&json=true","fetch_graph":"https://pith.science/api/pith-number/5L6ATRKVSSATYWYNTGRAMRDWCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/5L6ATRKVSSATYWYNTGRAMRDWCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ/action/storage_attestation","attest_author":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ/action/author_attestation","sign_citation":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ/action/citation_signature","submit_replication":"https://pith.science/pith/5L6ATRKVSSATYWYNTGRAMRDWCJ/action/replication_record"}},"created_at":"2026-07-05T07:59:49.146721+00:00","updated_at":"2026-07-05T07:59:49.146721+00:00"}