{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z5ILWRZBYD33IOB3HK2KBUFQUI","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":"f3b37ecafce8c7e27cf439ecd4c0f149c53ab91486e388c891fa65a42556f12e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-24T16:51:28Z","title_canon_sha256":"ee5a77de78010801b08f46d71247ca109a82f62af140ae2a6184008e6049815d"},"schema_version":"1.0","source":{"id":"1103.4807","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4807","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4807v2","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4807","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"Z5ILWRZBYD33","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z5ILWRZBYD33IOB3","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z5ILWRZB","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:9c82c87272830f4ede885585f84591327d82a823971b3847fb0fc1bccd62c653","target":"graph","created_at":"2026-05-18T03:57:37Z","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 study the distribution of the major index with sign on some parabolic quotients of the symmetric group, extending and generalizing simultaneously results Gessel-Simion and Adin-Gessel-Roichman, and on some special trees that we call rakes. We further consider and compute the distribution of the flag-major index on some parabolic quotients of wreath products and other related groups. All these distributions turn out to have very simple factorization formulas.","authors_text":"Fabrizio Caselli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-24T16:51:28Z","title":"Signed mahonians on some trees and parabolic quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4807","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":"sha256:117e6a21738ebecea203429680d46276cfff6a6d43012174865eeeded6a7f688","target":"record","created_at":"2026-05-18T03:57:37Z","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":"f3b37ecafce8c7e27cf439ecd4c0f149c53ab91486e388c891fa65a42556f12e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-24T16:51:28Z","title_canon_sha256":"ee5a77de78010801b08f46d71247ca109a82f62af140ae2a6184008e6049815d"},"schema_version":"1.0","source":{"id":"1103.4807","kind":"arxiv","version":2}},"canonical_sha256":"cf50bb4721c0f7b4383b3ab4a0d0b0a204c4051118e7bd899c7352d84526f4c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf50bb4721c0f7b4383b3ab4a0d0b0a204c4051118e7bd899c7352d84526f4c6","first_computed_at":"2026-05-18T03:57:37.307243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:37.307243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AHt8z2FsjCmFBmlWZg/l0eDCxc1hIJTsoSmWT/4Gf6LS6hXo3wg0yLGq39DMg6TmdiIqDjrgYJsAiNFC8yYBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:37.307984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4807","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:117e6a21738ebecea203429680d46276cfff6a6d43012174865eeeded6a7f688","sha256:9c82c87272830f4ede885585f84591327d82a823971b3847fb0fc1bccd62c653"],"state_sha256":"ee9a94fae2f5836ef0e5696511f0a76a89f1dd97f0dcaf07a1258b7bde3a9d90"}