{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UG2GLIPRS73OYQN6VY72CTJGZ5","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":"4247837d6b50bd384aced99bd084d2ca1158e47c558fccc9f31fb5931f66cc8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-30T04:30:19Z","title_canon_sha256":"9c82eec67cfdabd806ad906f508ce99a6ac4c455ff84ecf6a767c3c0059f19c2"},"schema_version":"1.0","source":{"id":"1304.7870","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7870","created_at":"2026-05-18T03:18:39Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7870v2","created_at":"2026-05-18T03:18:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7870","created_at":"2026-05-18T03:18:39Z"},{"alias_kind":"pith_short_12","alias_value":"UG2GLIPRS73O","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UG2GLIPRS73OYQN6","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UG2GLIPR","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:f4f6e7d101c2045ba359ec1b5410bd976624f3a209eb989235da745bdcb19e2d","target":"graph","created_at":"2026-05-18T03:18:39Z","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":"Generalizing the notion of a vexillary permutation, we introduce a filtration of S_infinity by the number of Schur function terms in the Stanley symmetric function, with the kth filtration level called the k-vexillary permutations. We show that for each k, the k-vexillary permutations are characterized by avoiding a finite set of patterns. A key step is the construction of a Specht series, in the sense of James and Peel, for the Specht module associated to the diagram of a permutation. As a corollary, we prove a conjecture of Liu on diagram varieties for certain classes of permutation diagrams","authors_text":"Brendan Pawlowski, Sara Billey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-30T04:30:19Z","title":"Permutation patterns, Stanley symmetric functions and generalized Specht modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7870","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":"sha256:3f6ae324d9f927da772c74af0feb52444b0625bc5a6de31ce049b450c280a11e","target":"record","created_at":"2026-05-18T03:18:39Z","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":"4247837d6b50bd384aced99bd084d2ca1158e47c558fccc9f31fb5931f66cc8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-30T04:30:19Z","title_canon_sha256":"9c82eec67cfdabd806ad906f508ce99a6ac4c455ff84ecf6a767c3c0059f19c2"},"schema_version":"1.0","source":{"id":"1304.7870","kind":"arxiv","version":2}},"canonical_sha256":"a1b465a1f197f6ec41beae3fa14d26cf773e2eaff816b0c20cf34d9464e06f0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1b465a1f197f6ec41beae3fa14d26cf773e2eaff816b0c20cf34d9464e06f0b","first_computed_at":"2026-05-18T03:18:39.965827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:39.965827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pl/4JflIceeUnbeta4SLRjHkjlpZAV2Jx4G1+gIKX34THhJjgxK6RI7ESeculfGN2kR+o01uJHBVboMyYIG+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:39.966634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7870","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f6ae324d9f927da772c74af0feb52444b0625bc5a6de31ce049b450c280a11e","sha256:f4f6e7d101c2045ba359ec1b5410bd976624f3a209eb989235da745bdcb19e2d"],"state_sha256":"bccb54b156e47af30512be88f9b1486955fceccd2a5c5c7f23e0985894821979"}