{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YT5O5Q4DUQQXJLPKWU3VRXBD3W","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":"97cc598ddecfe67387890f3ffdc3a62d0a44a4da9745afd6157c393389b058a2","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-16T20:30:25Z","title_canon_sha256":"2c6967c52e025b97fee2d59038656caba72d62ebebbd738a98a1076452c74b49"},"schema_version":"1.0","source":{"id":"1512.05319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05319","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05319v2","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05319","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"YT5O5Q4DUQQX","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YT5O5Q4DUQQXJLPK","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YT5O5Q4D","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:4a91af3bb8c34a9f490a92ab801c88fb733a1f799039e10a38c2c641f98870c1","target":"graph","created_at":"2026-05-18T01:04:37Z","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 present new efficient data structures for elements of Coxeter groups of type $A_m$ and their associated Iwahori--Hecke algebras $H(A_m)$. Usually, elements of $H(A_m)$ are represented as simple coefficient list of length $M = (m+1)!$ with respect to the standard basis, indexed by the elements of the Coxeter group. In the new data structure, elements of $H(A_m)$ are represented as nested coefficient lists. While the cost of addition is the same in both data structures, the new data structure leads to a huge improvement in the cost of multiplication in~$H(A_m)$.","authors_text":"Alice C. Niemeyer, Cheryl E. Praeger, G\\\"otz Pfeiffer","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-16T20:30:25Z","title":"On the Complexity of Multiplication in the Iwahori--Hecke Algebra of the Symmetric Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05319","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":"sha256:6f37207c68887f34c386837769e2cd1a40a1515820352858182b4a175e7a8aa9","target":"record","created_at":"2026-05-18T01:04:37Z","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":"97cc598ddecfe67387890f3ffdc3a62d0a44a4da9745afd6157c393389b058a2","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-16T20:30:25Z","title_canon_sha256":"2c6967c52e025b97fee2d59038656caba72d62ebebbd738a98a1076452c74b49"},"schema_version":"1.0","source":{"id":"1512.05319","kind":"arxiv","version":2}},"canonical_sha256":"c4faeec383a42174adeab53758dc23ddab4cf940bb68d1385638144ff511dea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4faeec383a42174adeab53758dc23ddab4cf940bb68d1385638144ff511dea1","first_computed_at":"2026-05-18T01:04:37.694654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:37.694654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6KkJUU4TF/TZmCNvazuHorv7Wpacf7pctOkr+lmtn5xXuRj6FYScySbqAwWK2mRRZTMQqHbCmcPKhvWALNpnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:37.695331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f37207c68887f34c386837769e2cd1a40a1515820352858182b4a175e7a8aa9","sha256:4a91af3bb8c34a9f490a92ab801c88fb733a1f799039e10a38c2c641f98870c1"],"state_sha256":"bc2fd4fabcbc2ae8652d2d71e51714c740454db5b8ef75c77b90e5fbaae778ff"}