{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:3ABK5AOXZUUKCDPTHT6K4NMRFJ","short_pith_number":"pith:3ABK5AOX","schema_version":"1.0","canonical_sha256":"d802ae81d7cd28a10df33cfcae35912a7f09f7f73dd7803225c20d9f30a82351","source":{"kind":"arxiv","id":"0811.2057","version":2},"attestation_state":"computed","paper":{"title":"The shifted plactic monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luis Serrano","submitted_at":"2008-11-13T09:43:08Z","abstract_excerpt":"We introduce a shifted analog of the plactic monoid of Lascoux and Sch\\\"utzenberger, the \\emph{shifted plactic monoid}. It can be defined in two different ways: via the \\emph{shifted Knuth relations}, or using Haiman's mixed insertion.\n  Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion of a Schur $P$-function; a shifted counterpart of the Lascoux-Sch\\\"utzenberger theory of noncommutative Schur functions in plactic variables; a characterization of shifted tableau words;"},"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":"0811.2057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-13T09:43:08Z","cross_cats_sorted":[],"title_canon_sha256":"9113cb7faa3b844e22227f851ca58676f1c7a1b8b9142ec22edc374bbc552ae9","abstract_canon_sha256":"a38a0f75e3673f63514fe5d2a442174104bca8c528b359c5763a2c614b3e734c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:36:26.040659Z","signature_b64":"J8XQ5OOpKVW3GApE8nx6hImEO2ybI1zGhIlwM/16yGh6s2+s6bwEi7le1XQP95VL/QE1qQvZ3feBsvT0f6gPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d802ae81d7cd28a10df33cfcae35912a7f09f7f73dd7803225c20d9f30a82351","last_reissued_at":"2026-07-04T15:36:26.040291Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:36:26.040291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The shifted plactic monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luis Serrano","submitted_at":"2008-11-13T09:43:08Z","abstract_excerpt":"We introduce a shifted analog of the plactic monoid of Lascoux and Sch\\\"utzenberger, the \\emph{shifted plactic monoid}. It can be defined in two different ways: via the \\emph{shifted Knuth relations}, or using Haiman's mixed insertion.\n  Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion of a Schur $P$-function; a shifted counterpart of the Lascoux-Sch\\\"utzenberger theory of noncommutative Schur functions in plactic variables; a characterization of shifted tableau words;"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2057","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/0811.2057/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":"0811.2057","created_at":"2026-07-04T15:36:26.040359+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.2057v2","created_at":"2026-07-04T15:36:26.040359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.2057","created_at":"2026-07-04T15:36:26.040359+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ABK5AOXZUUK","created_at":"2026-07-04T15:36:26.040359+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ABK5AOXZUUKCDPT","created_at":"2026-07-04T15:36:26.040359+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ABK5AOX","created_at":"2026-07-04T15:36:26.040359+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/3ABK5AOXZUUKCDPTHT6K4NMRFJ","json":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ.json","graph_json":"https://pith.science/api/pith-number/3ABK5AOXZUUKCDPTHT6K4NMRFJ/graph.json","events_json":"https://pith.science/api/pith-number/3ABK5AOXZUUKCDPTHT6K4NMRFJ/events.json","paper":"https://pith.science/paper/3ABK5AOX"},"agent_actions":{"view_html":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ","download_json":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ.json","view_paper":"https://pith.science/paper/3ABK5AOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.2057&json=true","fetch_graph":"https://pith.science/api/pith-number/3ABK5AOXZUUKCDPTHT6K4NMRFJ/graph.json","fetch_events":"https://pith.science/api/pith-number/3ABK5AOXZUUKCDPTHT6K4NMRFJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ/action/storage_attestation","attest_author":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ/action/author_attestation","sign_citation":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ/action/citation_signature","submit_replication":"https://pith.science/pith/3ABK5AOXZUUKCDPTHT6K4NMRFJ/action/replication_record"}},"created_at":"2026-07-04T15:36:26.040359+00:00","updated_at":"2026-07-04T15:36:26.040359+00:00"}