{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ALGIVK53YZU7YWAZSSCHM53J4D","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":"573f3ded7114aead8c6959b775b37425ad896ae2e2e578bfcbf918d2576697b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-04T15:39:32Z","title_canon_sha256":"a451e5b92df42eb1e28b7dc9b187eceb2015f8445620f62a0b4171071a53f7e9"},"schema_version":"1.0","source":{"id":"1506.01628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01628","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01628v2","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01628","created_at":"2026-05-18T00:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"ALGIVK53YZU7","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ALGIVK53YZU7YWAZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ALGIVK53","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:74ead39dc7f02a93acb12ac50aca14afd0f828c27ac0e54e809fcb987490c761","target":"graph","created_at":"2026-05-18T00:29:15Z","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 exponential generating function analogues to two classical identities involving the ordinary generating function of the complete homogeneous symmetric functions. After a suitable specialization the new identities reduce to identities involving the first and second order Eulerian polynomials. The study of these identities led us to consider a family of symmetric functions associated with a class of permutations introduced by Gessel and Stanley, known in the literature as Stirling permutations. In particular, we define certain type statistics on Stirling permutations that refine the s","authors_text":"Rafael S. Gonz\\'alez D'Le\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-04T15:39:32Z","title":"A family of symmetric functions associated with Stirling permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01628","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":"sha256:5cf9ffd55f25af3a067fdd084332b01f7f71dc12233e991b45658004b3a1e263","target":"record","created_at":"2026-05-18T00:29:15Z","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":"573f3ded7114aead8c6959b775b37425ad896ae2e2e578bfcbf918d2576697b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-04T15:39:32Z","title_canon_sha256":"a451e5b92df42eb1e28b7dc9b187eceb2015f8445620f62a0b4171071a53f7e9"},"schema_version":"1.0","source":{"id":"1506.01628","kind":"arxiv","version":2}},"canonical_sha256":"02cc8aabbbc669fc58199484767769e0d8a25d70936817e195152802377adb6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02cc8aabbbc669fc58199484767769e0d8a25d70936817e195152802377adb6f","first_computed_at":"2026-05-18T00:29:15.864530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:15.864530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W5ch1O/o7AwCv4ULxLIBOy828ITLgAkdb9nupioHlBFohNPSALptqArRxL+WZ/rY/z/nY81oG1kqUxo1BtGlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:15.865196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cf9ffd55f25af3a067fdd084332b01f7f71dc12233e991b45658004b3a1e263","sha256:74ead39dc7f02a93acb12ac50aca14afd0f828c27ac0e54e809fcb987490c761"],"state_sha256":"fe36636789aecbce4e973bf98f24045ce653ec12ea5375e2b8c7225d78e526fe"}