{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NB5ZPHVEFLXSJJNMTDHKQ74GVX","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":"43d0ace07ee7c1499377f11a9540d3007e9021905817317e9210b6a76daaa85a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-25T04:26:18Z","title_canon_sha256":"ac25c694ee5b0fca81b2525b0dff6d46186fe766a88e1cfeb5cdf25fc73aecb5"},"schema_version":"1.0","source":{"id":"1707.07809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07809","created_at":"2026-05-18T00:39:30Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07809v1","created_at":"2026-05-18T00:39:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07809","created_at":"2026-05-18T00:39:30Z"},{"alias_kind":"pith_short_12","alias_value":"NB5ZPHVEFLXS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NB5ZPHVEFLXSJJNM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NB5ZPHVE","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:ba6f96c66cfd23140e539d5fe6320066377ad6fb27819b656380ec4c94bca349","target":"graph","created_at":"2026-05-18T00:39:30Z","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":"We consider asymptotics of set partition pattern avoidance in the sense of Klazar. Our main result derives the asymptotics of the number of set partitions avoiding a given set partition within an exponential factor, which leads to a classification of possible growth rates of set partition pattern classes. We further define a notion of permutation-tuple avoidance, which generalizes notions of Aldred et al. and the usual permutation pattern setting, and similarly determine the number of permutation-tuples avoiding a given tuple to within an exponential factor.","authors_text":"Benjamin Gunby, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-25T04:26:18Z","title":"Asymptotics of Pattern Avoidance in the Klazar Set Partition and Permutation-Tuple Settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07809","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:b9caaeafadada3b3fa753982dbd25ba0f14440c9302cd78fe7475630eb4506bc","target":"record","created_at":"2026-05-18T00:39:30Z","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":"43d0ace07ee7c1499377f11a9540d3007e9021905817317e9210b6a76daaa85a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-25T04:26:18Z","title_canon_sha256":"ac25c694ee5b0fca81b2525b0dff6d46186fe766a88e1cfeb5cdf25fc73aecb5"},"schema_version":"1.0","source":{"id":"1707.07809","kind":"arxiv","version":1}},"canonical_sha256":"687b979ea42aef24a5ac98cea87f86add597a82bc05df83675dfe1a7d6d2f643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"687b979ea42aef24a5ac98cea87f86add597a82bc05df83675dfe1a7d6d2f643","first_computed_at":"2026-05-18T00:39:30.274127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:30.274127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qki5cpS+XdVE4In1KdfE8OJ2ICvhtMbNSbZ9/l1Vcu7t0NqRNHmwVPL1QgSh0ZZUeGdSULtgb9Oz6465HQuoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:30.274628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9caaeafadada3b3fa753982dbd25ba0f14440c9302cd78fe7475630eb4506bc","sha256:ba6f96c66cfd23140e539d5fe6320066377ad6fb27819b656380ec4c94bca349"],"state_sha256":"5093021fd8fa5a653f0f1eaeb29f9dd9ecc135e9b483ae824c54f8f1e20021e7"}