{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YLCSGM7Z6XUBSJ3QIPRF3KIG2S","short_pith_number":"pith:YLCSGM7Z","schema_version":"1.0","canonical_sha256":"c2c52333f9f5e819277043e25da906d498d03bf9719ced1b67774cc0af6c9c7a","source":{"kind":"arxiv","id":"1008.1514","version":1},"attestation_state":"computed","paper":{"title":"Moments of an exponential functional of random walks and permutations with given descent sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Balazs Szekely, Tamas Szabados","submitted_at":"2010-08-09T14:35:08Z","abstract_excerpt":"The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial $Y = 1 + \\xi_1 + \\xi_1 \\xi_2 + \\xi_1 \\xi_2 \\xi_3 + ...$ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables $\\mu_k = \\ev(\\xi^k) < 1$ with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triang"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.1514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-09T14:35:08Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e9706c3fe830bcf7c2b97de1fc67d840bd966535c0e3b81dc0e2ae008c73b693","abstract_canon_sha256":"dbba8f525297bfa03166f0d68268c37e947a942e6fd15cb1a6e6522d6b701399"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:24.077621Z","signature_b64":"tCf0vwE7+wS74ANPAK040ntCTU2o9ANrPafRuU8k7FGUIhtNqwqlNnCGzqqB4XUGAAmxPJW5JBZXGeVx9I+aCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2c52333f9f5e819277043e25da906d498d03bf9719ced1b67774cc0af6c9c7a","last_reissued_at":"2026-05-18T04:42:24.077220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:24.077220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moments of an exponential functional of random walks and permutations with given descent sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Balazs Szekely, Tamas Szabados","submitted_at":"2010-08-09T14:35:08Z","abstract_excerpt":"The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial $Y = 1 + \\xi_1 + \\xi_1 \\xi_2 + \\xi_1 \\xi_2 \\xi_3 + ...$ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables $\\mu_k = \\ev(\\xi^k) < 1$ with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1514","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.1514","created_at":"2026-05-18T04:42:24.077267+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.1514v1","created_at":"2026-05-18T04:42:24.077267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1514","created_at":"2026-05-18T04:42:24.077267+00:00"},{"alias_kind":"pith_short_12","alias_value":"YLCSGM7Z6XUB","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YLCSGM7Z6XUBSJ3Q","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YLCSGM7Z","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S","json":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S.json","graph_json":"https://pith.science/api/pith-number/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/graph.json","events_json":"https://pith.science/api/pith-number/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/events.json","paper":"https://pith.science/paper/YLCSGM7Z"},"agent_actions":{"view_html":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S","download_json":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S.json","view_paper":"https://pith.science/paper/YLCSGM7Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.1514&json=true","fetch_graph":"https://pith.science/api/pith-number/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/graph.json","fetch_events":"https://pith.science/api/pith-number/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/action/storage_attestation","attest_author":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/action/author_attestation","sign_citation":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/action/citation_signature","submit_replication":"https://pith.science/pith/YLCSGM7Z6XUBSJ3QIPRF3KIG2S/action/replication_record"}},"created_at":"2026-05-18T04:42:24.077267+00:00","updated_at":"2026-05-18T04:42:24.077267+00:00"}