{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E6ORKGTOI5EWBYHIT3RSNG454X","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":"a28f13acc47f8ea8054aade644ed537404e3086b57043c11d0c335987bdac5a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T09:14:53Z","title_canon_sha256":"3ec67d15bcbc187c4b940bff4c3787f07e80932c3910459b191b7ed142c283ab"},"schema_version":"1.0","source":{"id":"1503.03991","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03991","created_at":"2026-05-18T02:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03991v1","created_at":"2026-05-18T02:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03991","created_at":"2026-05-18T02:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"E6ORKGTOI5EW","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"E6ORKGTOI5EWBYHI","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"E6ORKGTO","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:4d0fbf853947dc7ca0330dd19ef043ea866ca05f2d0de4236cff3e227fe2ff41","target":"graph","created_at":"2026-05-18T02:23:57Z","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":"The aim of this work is to extend to a general $S_m\\times S_n$-module context the Grossman-Bizley paradigm that allows the enumeration of Dyck paths in a $m\\times n$-rectangle. We obtain an explicit formula for the the \"bi-Frobenius\" characteristic of what we call {\\em interlaced} rectangular parking functions in an $m\\times n$-rectangle. These are obtained by labelling the $n$ vertical steps of an $m\\times n$-Dyck path by the numbers from $1$ to $n$, together with an independent labelling of its horizontal steps by integers from $1$ to $m$. Our formula specializes to give the Frobenius charac","authors_text":"Fran\\c{c}ois Bergeron, Jean-Christophe Aval","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T09:14:53Z","title":"Interlaced rectangular parking functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03991","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:bee8d983e737c3eec519ac597f875f4a921e911fed590a714fd93aac8b2da4e4","target":"record","created_at":"2026-05-18T02:23:57Z","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":"a28f13acc47f8ea8054aade644ed537404e3086b57043c11d0c335987bdac5a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T09:14:53Z","title_canon_sha256":"3ec67d15bcbc187c4b940bff4c3787f07e80932c3910459b191b7ed142c283ab"},"schema_version":"1.0","source":{"id":"1503.03991","kind":"arxiv","version":1}},"canonical_sha256":"279d151a6e474960e0e89ee3269b9de5ee9df6a9331619cb0880347617505a21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"279d151a6e474960e0e89ee3269b9de5ee9df6a9331619cb0880347617505a21","first_computed_at":"2026-05-18T02:23:57.473368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:57.473368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JmmOfWV/OImUwDB9ce3Om5zQRrALHGyx1f2W3OgM2VSWx3ECSGfy0j8YQ+kobGJv1H8NVofFRZcDGTsKN7VgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:57.474018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03991","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bee8d983e737c3eec519ac597f875f4a921e911fed590a714fd93aac8b2da4e4","sha256:4d0fbf853947dc7ca0330dd19ef043ea866ca05f2d0de4236cff3e227fe2ff41"],"state_sha256":"73611c888f37bd594d819832a9a1f9f07472ad54fd2a31be6e9a623411515366"}