{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4XRMXBNUBVYXEDA2MUI74VNVBK","short_pith_number":"pith:4XRMXBNU","schema_version":"1.0","canonical_sha256":"e5e2cb85b40d71720c1a6511fe55b50aa5f62bbbca1e798545ef3779a8009389","source":{"kind":"arxiv","id":"1108.4379","version":1},"attestation_state":"computed","paper":{"title":"Excursions into Algebra and Combinatorics at $q=0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Tom Denton","submitted_at":"2011-08-22T17:05:05Z","abstract_excerpt":"We explore combinatorics associated with the degenerate Hecke algebra at $q=0$, obtaining a formula for a system of orthogonal idempotents, and also exploring various pattern avoidance results. Generalizing constructions for the 0-Hecke algebra, we explore the representation theory of $\\JJ$-trivial monoids.\n  We then discuss two-tensors of crystal bases for $U_q(\\tilde{\\mathfrak{sl}_2})$, establishing a complementary result to one of Bandlow, Schilling, and Thi\\'ery on affine crystals arising from promotion operators. Finally, we give a computer implementation of Stembridge's local axioms for "},"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":"1108.4379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-22T17:05:05Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"7bcf6067567e46a89e295e56c2dc5427e8dfa0ae5e6f2e02c81e46d0db636f04","abstract_canon_sha256":"9f9559c05dd407dc805125ffb9c193e69eec63a65923df7043173b93a9f2d95c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:24.938753Z","signature_b64":"hsb+PNTgVYYPIDqH3gf1kNjI1c3LQ0cVzPFmid8Kdd8nCBwWVEgyTRVg4q7UcSZoJiZhkzgXG7zB11zT3z8CCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5e2cb85b40d71720c1a6511fe55b50aa5f62bbbca1e798545ef3779a8009389","last_reissued_at":"2026-05-18T03:57:24.937920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:24.937920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Excursions into Algebra and Combinatorics at $q=0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Tom Denton","submitted_at":"2011-08-22T17:05:05Z","abstract_excerpt":"We explore combinatorics associated with the degenerate Hecke algebra at $q=0$, obtaining a formula for a system of orthogonal idempotents, and also exploring various pattern avoidance results. Generalizing constructions for the 0-Hecke algebra, we explore the representation theory of $\\JJ$-trivial monoids.\n  We then discuss two-tensors of crystal bases for $U_q(\\tilde{\\mathfrak{sl}_2})$, establishing a complementary result to one of Bandlow, Schilling, and Thi\\'ery on affine crystals arising from promotion operators. Finally, we give a computer implementation of Stembridge's local axioms for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4379","kind":"arxiv","version":1},"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":"1108.4379","created_at":"2026-05-18T03:57:24.938052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.4379v1","created_at":"2026-05-18T03:57:24.938052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4379","created_at":"2026-05-18T03:57:24.938052+00:00"},{"alias_kind":"pith_short_12","alias_value":"4XRMXBNUBVYX","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4XRMXBNUBVYXEDA2","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4XRMXBNU","created_at":"2026-05-18T12:26:20.644004+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/4XRMXBNUBVYXEDA2MUI74VNVBK","json":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK.json","graph_json":"https://pith.science/api/pith-number/4XRMXBNUBVYXEDA2MUI74VNVBK/graph.json","events_json":"https://pith.science/api/pith-number/4XRMXBNUBVYXEDA2MUI74VNVBK/events.json","paper":"https://pith.science/paper/4XRMXBNU"},"agent_actions":{"view_html":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK","download_json":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK.json","view_paper":"https://pith.science/paper/4XRMXBNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.4379&json=true","fetch_graph":"https://pith.science/api/pith-number/4XRMXBNUBVYXEDA2MUI74VNVBK/graph.json","fetch_events":"https://pith.science/api/pith-number/4XRMXBNUBVYXEDA2MUI74VNVBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK/action/storage_attestation","attest_author":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK/action/author_attestation","sign_citation":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK/action/citation_signature","submit_replication":"https://pith.science/pith/4XRMXBNUBVYXEDA2MUI74VNVBK/action/replication_record"}},"created_at":"2026-05-18T03:57:24.938052+00:00","updated_at":"2026-05-18T03:57:24.938052+00:00"}