{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:5VK5F5PCBTNJFGBX564S2B2JTT","short_pith_number":"pith:5VK5F5PC","schema_version":"1.0","canonical_sha256":"ed55d2f5e20cda929837efb92d07499cdd0d2920f22394ff8f772ed60bcdcbcc","source":{"kind":"arxiv","id":"2412.18058","version":1},"attestation_state":"computed","paper":{"title":"Robinson-Schensted shapes arising from cycle decompositions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonathan Feigert, Jonathan Meddaugh, Kyle Rosengartner, Mark R. Sepanski, Markus Hunziker, Martha Du Preez, Mitchell Minyard, William Q. Erickson","submitted_at":"2024-12-24T00:08:02Z","abstract_excerpt":"In the symmetric group $S_n$, each element $\\sigma$ has an associated cycle type $\\alpha$, a partition of $n$ that identifies the conjugacy class of $\\sigma$. The Robinson-Schensted (RS) correspondence links each $\\sigma$ to another partition $\\lambda$ of $n$, representing the shape of the pair of Young tableaux produced by applying the RS row-insertion algorithm to $\\sigma$. Surprisingly, the relationship between these two partitions, namely the cycle type $\\alpha$ and the RS shape $\\lambda$, has only recently become a subject of study. In this work, we explicitly describe the set of RS shape"},"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":"2412.18058","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-12-24T00:08:02Z","cross_cats_sorted":[],"title_canon_sha256":"4946e99cf1b7bbdeb372ce102c2df18b76a98fbfe02152d85240aacc7e0081aa","abstract_canon_sha256":"609a6f750a5f3db073fbfb24b15340db62599d0ec1a3664b05724e56ac0081ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:49.025173Z","signature_b64":"q84vkRx1QviJaXzH+Rm+5UJrt5bfSa6ANTNHrchPTm99XofcQZQO/OpBhaA9xixPIFmbO45vM51+A6rE/BziDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed55d2f5e20cda929837efb92d07499cdd0d2920f22394ff8f772ed60bcdcbcc","last_reissued_at":"2026-07-05T09:53:49.024805Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:49.024805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robinson-Schensted shapes arising from cycle decompositions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonathan Feigert, Jonathan Meddaugh, Kyle Rosengartner, Mark R. Sepanski, Markus Hunziker, Martha Du Preez, Mitchell Minyard, William Q. Erickson","submitted_at":"2024-12-24T00:08:02Z","abstract_excerpt":"In the symmetric group $S_n$, each element $\\sigma$ has an associated cycle type $\\alpha$, a partition of $n$ that identifies the conjugacy class of $\\sigma$. The Robinson-Schensted (RS) correspondence links each $\\sigma$ to another partition $\\lambda$ of $n$, representing the shape of the pair of Young tableaux produced by applying the RS row-insertion algorithm to $\\sigma$. Surprisingly, the relationship between these two partitions, namely the cycle type $\\alpha$ and the RS shape $\\lambda$, has only recently become a subject of study. In this work, we explicitly describe the set of RS shape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18058","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.18058/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":"2412.18058","created_at":"2026-07-05T09:53:49.024860+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.18058v1","created_at":"2026-07-05T09:53:49.024860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18058","created_at":"2026-07-05T09:53:49.024860+00:00"},{"alias_kind":"pith_short_12","alias_value":"5VK5F5PCBTNJ","created_at":"2026-07-05T09:53:49.024860+00:00"},{"alias_kind":"pith_short_16","alias_value":"5VK5F5PCBTNJFGBX","created_at":"2026-07-05T09:53:49.024860+00:00"},{"alias_kind":"pith_short_8","alias_value":"5VK5F5PC","created_at":"2026-07-05T09:53:49.024860+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/5VK5F5PCBTNJFGBX564S2B2JTT","json":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT.json","graph_json":"https://pith.science/api/pith-number/5VK5F5PCBTNJFGBX564S2B2JTT/graph.json","events_json":"https://pith.science/api/pith-number/5VK5F5PCBTNJFGBX564S2B2JTT/events.json","paper":"https://pith.science/paper/5VK5F5PC"},"agent_actions":{"view_html":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT","download_json":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT.json","view_paper":"https://pith.science/paper/5VK5F5PC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.18058&json=true","fetch_graph":"https://pith.science/api/pith-number/5VK5F5PCBTNJFGBX564S2B2JTT/graph.json","fetch_events":"https://pith.science/api/pith-number/5VK5F5PCBTNJFGBX564S2B2JTT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT/action/storage_attestation","attest_author":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT/action/author_attestation","sign_citation":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT/action/citation_signature","submit_replication":"https://pith.science/pith/5VK5F5PCBTNJFGBX564S2B2JTT/action/replication_record"}},"created_at":"2026-07-05T09:53:49.024860+00:00","updated_at":"2026-07-05T09:53:49.024860+00:00"}