{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EN7OWMZUJ2WXHCLUTVLSW5BSYE","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":"d2157a2b838e8fcf392822a2a0031a37c82eb80b0ea07d8fef51d7faa4343301","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-21T06:08:39Z","title_canon_sha256":"862e717d086641f93220117504503fba2e3520cde68a12aa4ad9baf1220ccfcf"},"schema_version":"1.0","source":{"id":"1402.5211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5211","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5211v1","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5211","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"EN7OWMZUJ2WX","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EN7OWMZUJ2WXHCLU","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EN7OWMZU","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:e60abeafb19ab79a363adbdf07e1f5a6a0581d707284b8b15fa4cbf2a8b36697","target":"graph","created_at":"2026-05-18T02:58:22Z","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":"In 2012, Sagan and Savage introduced the notion of $st$-Wilf equivalence for a statistic $st$ and for sets of permutations that avoid particular permutation patterns which can be extended to generalized permutation patterns. In this paper we consider $inv$-Wilf equivalence on sets of two or more consecutive permutation patterns. We say that two sets of generalized permutation patterns $\\Pi$ and $\\Pi'$ are $inv$-Wilf equivalent if the generating function for the inversion statistic on the permutations that simultaneously avoid all elements of $\\Pi$ is equal to the generating function for the in","authors_text":"Kendra Killpatrick, Naiomi Cameron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-21T06:08:39Z","title":"Inversion Polynomials for Permutations Avoiding Consecutive Patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5211","kind":"arxiv","version":1},"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:a4a58c9eae758f25c765728c68e0cbdab234d51557850652f927043eebbccab8","target":"record","created_at":"2026-05-18T02:58:22Z","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":"d2157a2b838e8fcf392822a2a0031a37c82eb80b0ea07d8fef51d7faa4343301","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-21T06:08:39Z","title_canon_sha256":"862e717d086641f93220117504503fba2e3520cde68a12aa4ad9baf1220ccfcf"},"schema_version":"1.0","source":{"id":"1402.5211","kind":"arxiv","version":1}},"canonical_sha256":"237eeb33344ead7389749d572b7432c12f78337191796c4c970e719dae891949","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"237eeb33344ead7389749d572b7432c12f78337191796c4c970e719dae891949","first_computed_at":"2026-05-18T02:58:22.818633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:22.818633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQ6beWkjdnywju/CP/dMJer+iFbLdb3ZUdnV1DjbA6iWqFSfPZZFjhi5AdSqPeVtdZZ2LaQkq3kvsNvCNCb7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:22.819245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4a58c9eae758f25c765728c68e0cbdab234d51557850652f927043eebbccab8","sha256:e60abeafb19ab79a363adbdf07e1f5a6a0581d707284b8b15fa4cbf2a8b36697"],"state_sha256":"64fd136bc4f8b8c0298e0ff957c2a146f68cb74183675f5cba71687cc596c8fc"}