{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ELLOY5CH7P2WWPI25J22A6JGIO","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":"7a7f37d8b9ea0581b6ebc3efe89218ea1bdf9069ebf3c90226850d80c98e619d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-07T19:47:14Z","title_canon_sha256":"487dc415927a37aec84abafad2f61ca6bf15acdad1e5c33f8c855955b48bc677"},"schema_version":"1.0","source":{"id":"1504.01719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01719","created_at":"2026-05-18T02:19:26Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01719v1","created_at":"2026-05-18T02:19:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01719","created_at":"2026-05-18T02:19:26Z"},{"alias_kind":"pith_short_12","alias_value":"ELLOY5CH7P2W","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ELLOY5CH7P2WWPI2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ELLOY5CH","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:9c55795526f46f882d724ce4b5cfc4792c6e3487bc999aadccb73cfae9bc9674","target":"graph","created_at":"2026-05-18T02:19:26Z","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":"Consider the vector space $\\mathbb{K}\\mathcal{P}$ spanned by parking functions. By representing parking functions as labeled digraphs, Hivert, Novelli and Thibon constructed a cocommutative Hopf algebra PQSym$^{*}$ on $\\mathbb{K}\\mathcal{P}$. The product and coproduct of PQSym$^{*}$ are analogous to the product and coproduct of the Hopf algebra NCSym of symmetric functions in noncommuting variables defined in terms of the power sum basis. In this paper, we view a parking function as a word. We shall construct a Hopf algebra PFSym on $\\mathbb{K}\\mathcal{P}$ with a formal basis $\\{M_a\\}$ analogo","authors_text":"Teresa Xueshan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-07T19:47:14Z","title":"The monomial basis and the $Q$-basis of the Hopf algebra of parking functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01719","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:b3f8f83b7a20d31929df3112b59d710f4b0b573ef7ea2814167df1673f885bbe","target":"record","created_at":"2026-05-18T02:19:26Z","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":"7a7f37d8b9ea0581b6ebc3efe89218ea1bdf9069ebf3c90226850d80c98e619d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-07T19:47:14Z","title_canon_sha256":"487dc415927a37aec84abafad2f61ca6bf15acdad1e5c33f8c855955b48bc677"},"schema_version":"1.0","source":{"id":"1504.01719","kind":"arxiv","version":1}},"canonical_sha256":"22d6ec7447fbf56b3d1aea75a079264395b17ace89c6b0e09c302fba821d21b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22d6ec7447fbf56b3d1aea75a079264395b17ace89c6b0e09c302fba821d21b4","first_computed_at":"2026-05-18T02:19:26.346870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:26.346870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wr5KeMz7yc+rBU7jBiuK1yfzO2WSuRJlsgSO00rbUX10tZpe3Q5e9XA0tCmqsCAm9vNVq8fJFCEWSdxCg25KCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:26.347758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3f8f83b7a20d31929df3112b59d710f4b0b573ef7ea2814167df1673f885bbe","sha256:9c55795526f46f882d724ce4b5cfc4792c6e3487bc999aadccb73cfae9bc9674"],"state_sha256":"a9226bf460fb130c2706963c70648c7c4ac3b4628fc5fb02d060cf73387545f3"}