{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IBRH5O77FOBH7OXEGSSYD5QVZK","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":"7423b2644677113dd5dccd2600ba376c006a6302f85b80b47188de581d9d407b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-03T11:59:50Z","title_canon_sha256":"a88f5d1adbd1094cdd74096d846983320877f0a7e5ba7f274b1e658bdf7213b2"},"schema_version":"1.0","source":{"id":"1301.0430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0430","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0430v1","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0430","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"IBRH5O77FOBH","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IBRH5O77FOBH7OXE","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IBRH5O77","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:c334fc6b9a9f5aab685b42736caa3e01aa79efee49554d9b26ac5df3b47f9554","target":"graph","created_at":"2026-05-18T03:37:19Z","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":"Given a permutation statistic $s : S_n \\to \\mathbb{R}$, define the mean statistic $\\bar{s}$ as the statistic which computes the mean of $s$ over conjugacy classes. We describe a way to calculate the expected value of $s$ on a product of $t$ independently chosen elements from the uniform distribution on a union of conjugacy classes $\\Gamma \\subseteq S_n$. In order to apply the formula, one needs to express the class function $\\bar{s}$ as a linear combination of irreducible $S_n$-characters. We provide such expressions for several commonly studied permutation statistics, including the excedance ","authors_text":"Axel Hultman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-03T11:59:50Z","title":"Permutation statistics of products of random permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0430","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":"sha256:895d2e59754b67c08983292ccf4f7fe1c8116aaf10dd92d7f086111ccbd5acf2","target":"record","created_at":"2026-05-18T03:37:19Z","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":"7423b2644677113dd5dccd2600ba376c006a6302f85b80b47188de581d9d407b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-03T11:59:50Z","title_canon_sha256":"a88f5d1adbd1094cdd74096d846983320877f0a7e5ba7f274b1e658bdf7213b2"},"schema_version":"1.0","source":{"id":"1301.0430","kind":"arxiv","version":1}},"canonical_sha256":"40627ebbff2b827fbae434a581f615caab5596412c7f5cf32d56838484c3f17b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40627ebbff2b827fbae434a581f615caab5596412c7f5cf32d56838484c3f17b","first_computed_at":"2026-05-18T03:37:19.664409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:19.664409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJXgHxBOBn6FgMsB3iIRUDFdbhbbLa7mp+KPZlkDKtoNK8ZOY5/Z3CJ1yq/PiUXEUsr3exdSMsZ37p8Yrry9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:19.664807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:895d2e59754b67c08983292ccf4f7fe1c8116aaf10dd92d7f086111ccbd5acf2","sha256:c334fc6b9a9f5aab685b42736caa3e01aa79efee49554d9b26ac5df3b47f9554"],"state_sha256":"8a2a14338b8efb69e696ea578be5e3233d1b320ca7cd9c74a4b396e326fcff60"}