{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SM2LZUGHSTJSFKEO23YXX7T46O","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":"d5487470e2f83c5ee266bdcab5abf2f4f323478e3d60e71457bc0e01496f754c","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-10T23:28:08Z","title_canon_sha256":"b236983b1630b002c2e6aa10382c92132805773a360e91413a31c6371b2035ca"},"schema_version":"1.0","source":{"id":"1009.2119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2119","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2119v2","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2119","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"SM2LZUGHSTJS","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SM2LZUGHSTJSFKEO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SM2LZUGH","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:668031b8cba9a0b845154fb86c042d2e31ff3e4784b683bcd9761616988ec16a","target":"graph","created_at":"2026-05-18T04:11:08Z","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 the problem of enumerating permutations in the symmetric group on $n$ elements which avoid a given set of consecutive pattern $S$, and in particular computing asymptotics as $n$ tends to infinity. We develop a general method which solves this enumeration problem using the spectral theory of integral operators on $L^{2}([0,1]^{m})$, where the patterns in $S$ has length $m+1$. Kre\\u{\\i}n and Rutman's generalization of the Perron--Frobenius theory of non-negative matrices plays a central role. Our methods give detailed asymptotic expansions and allow for explicit computation of leadin","authors_text":"Peter Perry, Richard Ehrenborg, Sergey Kitaev","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-10T23:28:08Z","title":"A Spectral Approach to Consecutive Pattern-Avoiding Permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2119","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":"sha256:820298aafe9e81a993eb9121caef2d83f2520d0d3876e824ee86d46d07cc9ed8","target":"record","created_at":"2026-05-18T04:11:08Z","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":"d5487470e2f83c5ee266bdcab5abf2f4f323478e3d60e71457bc0e01496f754c","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-10T23:28:08Z","title_canon_sha256":"b236983b1630b002c2e6aa10382c92132805773a360e91413a31c6371b2035ca"},"schema_version":"1.0","source":{"id":"1009.2119","kind":"arxiv","version":2}},"canonical_sha256":"9334bcd0c794d322a88ed6f17bfe7cf3bdf61d097bfd82e556c705fb86ac7870","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9334bcd0c794d322a88ed6f17bfe7cf3bdf61d097bfd82e556c705fb86ac7870","first_computed_at":"2026-05-18T04:11:08.853053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:08.853053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BwWbNitMQK4kc7u8ARjq6xNI5iiy4zzZCNDPsYB7S1niQluNWIk0e8y3djMU4OMJ1pk1kZx7KNFWC8rHN5ABCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:08.853538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:820298aafe9e81a993eb9121caef2d83f2520d0d3876e824ee86d46d07cc9ed8","sha256:668031b8cba9a0b845154fb86c042d2e31ff3e4784b683bcd9761616988ec16a"],"state_sha256":"c1d5be659c38ba77eb3a3bd2b68df0818b3fe759d924f169ed7c32391faefbd4"}