{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XZJLTCSAYK4JQJ5FFXNCWKQXGS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c2e96913b4dacda574332a4c45e8c248680d789aba413b0fdf1f74ecb93c18e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-05T10:56:47Z","title_canon_sha256":"bcb91060e0611a8ff141133e9b6ff94ace2d8a88b686c5ea1d97c41784b41a9c"},"schema_version":"1.0","source":{"id":"1308.0936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0936","created_at":"2026-05-18T03:14:49Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0936v2","created_at":"2026-05-18T03:14:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0936","created_at":"2026-05-18T03:14:49Z"},{"alias_kind":"pith_short_12","alias_value":"XZJLTCSAYK4J","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XZJLTCSAYK4JQJ5F","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XZJLTCSA","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:ad1ba488d4ae8345ebdd714a8efcc9047bdab0ce0a09a27165ad289684f74405","target":"graph","created_at":"2026-05-18T03:14:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The purpose of this article is to initiate a combinatorial study of the Bruhat-Chevalley ordering on certain sets of permutations obtained by omitting the parentheses from their standard cyclic notation. In particular, we show that these sets form a bounded, graded, unimodal, rank-symmetric and EL-shellable posets. Moreover, we determine the homotopy types of the associated order complexes.","authors_text":"Mahir Bilen Can, Yonah Cherniavsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-05T10:56:47Z","title":"Omitting parentheses from the cyclic notation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0936","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:986e214b159587e7d51e4e67add676e3c22cf72cbad1e2c368093905d770f6ac","target":"record","created_at":"2026-05-18T03:14:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c2e96913b4dacda574332a4c45e8c248680d789aba413b0fdf1f74ecb93c18e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-05T10:56:47Z","title_canon_sha256":"bcb91060e0611a8ff141133e9b6ff94ace2d8a88b686c5ea1d97c41784b41a9c"},"schema_version":"1.0","source":{"id":"1308.0936","kind":"arxiv","version":2}},"canonical_sha256":"be52b98a40c2b89827a52dda2b2a1734a0fee89e811f00721b9ed1720ecbdf55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be52b98a40c2b89827a52dda2b2a1734a0fee89e811f00721b9ed1720ecbdf55","first_computed_at":"2026-05-18T03:14:49.558758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:49.558758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NCTQL92smuEjl3BD7rFXlRrijsqEgg0hqFERHv+fi6UmhFfDGt0QJIfB3GZJCEqjI6i6Dc0xJY4bHDpu5oz5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:49.559396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:986e214b159587e7d51e4e67add676e3c22cf72cbad1e2c368093905d770f6ac","sha256:ad1ba488d4ae8345ebdd714a8efcc9047bdab0ce0a09a27165ad289684f74405"],"state_sha256":"5e4921cd7cd048003b78e79559cdc76d0be9901fd482b3de512cc5dda6bc3b5c"}