{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MZ2TXRACBXAE36NLIE7R6ZTP2S","short_pith_number":"pith:MZ2TXRAC","canonical_record":{"source":{"id":"1904.11437","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-25T16:19:36Z","cross_cats_sorted":[],"title_canon_sha256":"d4c81b8e77ce84d0b68ba744cf3c304d510667900e75c3e8c975ee5f00653fc9","abstract_canon_sha256":"dc6eea82552e5102f46e409e56e5f80e725be3df35dd6f140a564af3d3da4275"},"schema_version":"1.0"},"canonical_sha256":"66753bc4020dc04df9ab413f1f666fd48f627c60bc0871ea8fcbede9e9f9a1db","source":{"kind":"arxiv","id":"1904.11437","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11437","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11437v3","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11437","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"MZ2TXRACBXAE","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MZ2TXRACBXAE36NL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MZ2TXRAC","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MZ2TXRACBXAE36NLIE7R6ZTP2S","target":"record","payload":{"canonical_record":{"source":{"id":"1904.11437","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-25T16:19:36Z","cross_cats_sorted":[],"title_canon_sha256":"d4c81b8e77ce84d0b68ba744cf3c304d510667900e75c3e8c975ee5f00653fc9","abstract_canon_sha256":"dc6eea82552e5102f46e409e56e5f80e725be3df35dd6f140a564af3d3da4275"},"schema_version":"1.0"},"canonical_sha256":"66753bc4020dc04df9ab413f1f666fd48f627c60bc0871ea8fcbede9e9f9a1db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:24.684363Z","signature_b64":"nrwldFRkfuCNKlmvpq/LeZlo08hShaAiRO3t4spmrrj/X9ftkrwj+gBJX0usNnVnEc9Pxa+JJ1riIdZvEHS+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66753bc4020dc04df9ab413f1f666fd48f627c60bc0871ea8fcbede9e9f9a1db","last_reissued_at":"2026-05-17T23:47:24.683717Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:24.683717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.11437","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o7O91z24DDmsLWaj9w2XWpxLlgJwsnAG2EV4OjfpFjvgA8Ft/EwHMjSpj6uXstgl4CwHiNEmi+ZrcXZ7/U4hDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:52:59.777300Z"},"content_sha256":"1cc37cb3667b2282f8c319410080cd83001ca66b5e0a3582ee99a0d78b0c608a","schema_version":"1.0","event_id":"sha256:1cc37cb3667b2282f8c319410080cd83001ca66b5e0a3582ee99a0d78b0c608a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MZ2TXRACBXAE36NLIE7R6ZTP2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The alternating run polynomials of permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun Ma, Shi-Mei Ma, Yeong-Nan Yeh","submitted_at":"2019-04-25T16:19:36Z","abstract_excerpt":"In this paper, we first consider a generalization of the David-Barton identity which relate the alternating run polynomials to Eulerian polynomials. By using context-free grammars, we then present a combinatorial interpretation of a family of q-alternating run polynomials. Furthermore, we introduce the definition of semi-gamma-positive polynomial and we show the semi-gamma-positivity of the alternating run polynomials of dual Stirling permutations. A connection between the up-down run polynomials of permutations and the alternating run polynomials of dual Stirling permutations is established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11437","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rr+L9g/09LOFj7q8jhac+Fw1LGj8SnLhgKyx8yq22i/VMq4I63Q3FGh1b7A3cVvqm8CpNtEzEAkuJsPRgESCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:52:59.777670Z"},"content_sha256":"a4b528ee67122333a0041b2458d0ad60e5605d7a2ffcf9d5cb066228f5e159b1","schema_version":"1.0","event_id":"sha256:a4b528ee67122333a0041b2458d0ad60e5605d7a2ffcf9d5cb066228f5e159b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZ2TXRACBXAE36NLIE7R6ZTP2S/bundle.json","state_url":"https://pith.science/pith/MZ2TXRACBXAE36NLIE7R6ZTP2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZ2TXRACBXAE36NLIE7R6ZTP2S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T17:52:59Z","links":{"resolver":"https://pith.science/pith/MZ2TXRACBXAE36NLIE7R6ZTP2S","bundle":"https://pith.science/pith/MZ2TXRACBXAE36NLIE7R6ZTP2S/bundle.json","state":"https://pith.science/pith/MZ2TXRACBXAE36NLIE7R6ZTP2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZ2TXRACBXAE36NLIE7R6ZTP2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MZ2TXRACBXAE36NLIE7R6ZTP2S","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":"dc6eea82552e5102f46e409e56e5f80e725be3df35dd6f140a564af3d3da4275","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-25T16:19:36Z","title_canon_sha256":"d4c81b8e77ce84d0b68ba744cf3c304d510667900e75c3e8c975ee5f00653fc9"},"schema_version":"1.0","source":{"id":"1904.11437","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11437","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11437v3","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11437","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"MZ2TXRACBXAE","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MZ2TXRACBXAE36NL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MZ2TXRAC","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:a4b528ee67122333a0041b2458d0ad60e5605d7a2ffcf9d5cb066228f5e159b1","target":"graph","created_at":"2026-05-17T23:47:24Z","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":"In this paper, we first consider a generalization of the David-Barton identity which relate the alternating run polynomials to Eulerian polynomials. By using context-free grammars, we then present a combinatorial interpretation of a family of q-alternating run polynomials. Furthermore, we introduce the definition of semi-gamma-positive polynomial and we show the semi-gamma-positivity of the alternating run polynomials of dual Stirling permutations. A connection between the up-down run polynomials of permutations and the alternating run polynomials of dual Stirling permutations is established.","authors_text":"Jun Ma, Shi-Mei Ma, Yeong-Nan Yeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-25T16:19:36Z","title":"The alternating run polynomials of permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11437","kind":"arxiv","version":3},"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":"sha256:1cc37cb3667b2282f8c319410080cd83001ca66b5e0a3582ee99a0d78b0c608a","target":"record","created_at":"2026-05-17T23:47:24Z","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":"dc6eea82552e5102f46e409e56e5f80e725be3df35dd6f140a564af3d3da4275","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-25T16:19:36Z","title_canon_sha256":"d4c81b8e77ce84d0b68ba744cf3c304d510667900e75c3e8c975ee5f00653fc9"},"schema_version":"1.0","source":{"id":"1904.11437","kind":"arxiv","version":3}},"canonical_sha256":"66753bc4020dc04df9ab413f1f666fd48f627c60bc0871ea8fcbede9e9f9a1db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66753bc4020dc04df9ab413f1f666fd48f627c60bc0871ea8fcbede9e9f9a1db","first_computed_at":"2026-05-17T23:47:24.683717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:24.683717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nrwldFRkfuCNKlmvpq/LeZlo08hShaAiRO3t4spmrrj/X9ftkrwj+gBJX0usNnVnEc9Pxa+JJ1riIdZvEHS+BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:24.684363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11437","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cc37cb3667b2282f8c319410080cd83001ca66b5e0a3582ee99a0d78b0c608a","sha256:a4b528ee67122333a0041b2458d0ad60e5605d7a2ffcf9d5cb066228f5e159b1"],"state_sha256":"cf5f0bcdb4f707fa78f27d5d8118e65f98a0b7efc4780d5e5471774d1b8fee9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTcbXqdt07aB/jBhVTyLe4ocp3i4LGEj+DMlNYh1oXpcDtAsC125usXT1QxR9+tqawy6OlI0GsfDM9PXVmRoCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:52:59.779603Z","bundle_sha256":"0c1c52fe0a5af4cce7b7fdcfe6fbdda27c10e99a26dd5a4acb61504956d3859a"}}