{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HALIII5CDEJOLSVNC6GSK3HLPW","short_pith_number":"pith:HALIII5C","schema_version":"1.0","canonical_sha256":"38168423a21912e5caad178d256ceb7da0913f115fcafd622511320733f89736","source":{"kind":"arxiv","id":"1609.07335","version":1},"attestation_state":"computed","paper":{"title":"On rotated Schur-positive sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sergi Elizalde, Yuval Roichman","submitted_at":"2016-09-23T12:29:12Z","abstract_excerpt":"The problem of finding Schur-positive sets of permutations, originally posed by Gessel and Reutenauer, has seen some recent developments. Schur-positive sets of pattern-avoiding permutations have been found by Sagan et al and a general construction based on geometric operations on grid classes has been given by the authors. In this paper we prove that horizontal rotations of Schur-positive subsets of permutations are always Schur-positive. The proof applies a cyclic action on standard Young tableaux of certain skew shapes and a jeu-de-taquin type straightening algorithm. As a consequence of th"},"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":"1609.07335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-23T12:29:12Z","cross_cats_sorted":[],"title_canon_sha256":"3745164511c4066732375c7942f702f7ff0c44f047c1ff3d6741239211c64b7d","abstract_canon_sha256":"01e4b70a7ac18fb9614ed999221100361a435460165acbdb01fa2e4939ece7c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:01.621079Z","signature_b64":"dq6rcC22jtU0Why3wuC+JBACqeBuL1itoa3pc/ABmtMD7OccBHVK6x7ywEgVwVGudgM48KOfVp/KPVzzksQnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38168423a21912e5caad178d256ceb7da0913f115fcafd622511320733f89736","last_reissued_at":"2026-05-18T01:04:01.620397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:01.620397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On rotated Schur-positive sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sergi Elizalde, Yuval Roichman","submitted_at":"2016-09-23T12:29:12Z","abstract_excerpt":"The problem of finding Schur-positive sets of permutations, originally posed by Gessel and Reutenauer, has seen some recent developments. Schur-positive sets of pattern-avoiding permutations have been found by Sagan et al and a general construction based on geometric operations on grid classes has been given by the authors. In this paper we prove that horizontal rotations of Schur-positive subsets of permutations are always Schur-positive. The proof applies a cyclic action on standard Young tableaux of certain skew shapes and a jeu-de-taquin type straightening algorithm. As a consequence of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07335","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":"1609.07335","created_at":"2026-05-18T01:04:01.620503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07335v1","created_at":"2026-05-18T01:04:01.620503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07335","created_at":"2026-05-18T01:04:01.620503+00:00"},{"alias_kind":"pith_short_12","alias_value":"HALIII5CDEJO","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HALIII5CDEJOLSVN","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HALIII5C","created_at":"2026-05-18T12:30:19.053100+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/HALIII5CDEJOLSVNC6GSK3HLPW","json":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW.json","graph_json":"https://pith.science/api/pith-number/HALIII5CDEJOLSVNC6GSK3HLPW/graph.json","events_json":"https://pith.science/api/pith-number/HALIII5CDEJOLSVNC6GSK3HLPW/events.json","paper":"https://pith.science/paper/HALIII5C"},"agent_actions":{"view_html":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW","download_json":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW.json","view_paper":"https://pith.science/paper/HALIII5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07335&json=true","fetch_graph":"https://pith.science/api/pith-number/HALIII5CDEJOLSVNC6GSK3HLPW/graph.json","fetch_events":"https://pith.science/api/pith-number/HALIII5CDEJOLSVNC6GSK3HLPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW/action/storage_attestation","attest_author":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW/action/author_attestation","sign_citation":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW/action/citation_signature","submit_replication":"https://pith.science/pith/HALIII5CDEJOLSVNC6GSK3HLPW/action/replication_record"}},"created_at":"2026-05-18T01:04:01.620503+00:00","updated_at":"2026-05-18T01:04:01.620503+00:00"}