{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HEVJNO5NSEW3RVTDCDTEV3O5UK","short_pith_number":"pith:HEVJNO5N","schema_version":"1.0","canonical_sha256":"392a96bbad912db8d66310e64aeddda2beb2e13fa1380da4607bfcf3d6428ec0","source":{"kind":"arxiv","id":"1701.00928","version":1},"attestation_state":"computed","paper":{"title":"Counting Lyndon factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen, Jamie Simpson, W. F. Smyth","submitted_at":"2017-01-04T08:19:56Z","abstract_excerpt":"In this paper, we determine the maximum number of distinct Lyndon factors that a word of length $n$ can contain. We also derive formulas for the expected total number of Lyndon factors in a word of length $n$ on an alphabet of size $\\sigma$, as well as the expected number of distinct Lyndon factors in such a word. The minimum number of distinct Lyndon factors in a word of length $n$ is $1$ and the minimum total number is $n$, with both bounds being achieved by $x^n$ where $x$ is a letter. A more interesting question to ask is what is the minimum number of distinct Lyndon factors in a Lyndon wo"},"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":"1701.00928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-04T08:19:56Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"53ba683009403f9a0937602742bec4981452823828d3fa90842705bcbe3e68b4","abstract_canon_sha256":"98f1321902793f650f1616cae690098d9bdf216de4ad64673dc470ee0a8f17a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:21.881243Z","signature_b64":"aKxY4JjK0XFLEmQvaJcJK384gmpc7aYKVnmQ+YIg9vYbp5A2Dq+1VIJu25P3nbe4ubDPOhBvPVZYFB+Xf9NfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"392a96bbad912db8d66310e64aeddda2beb2e13fa1380da4607bfcf3d6428ec0","last_reissued_at":"2026-05-18T00:53:21.880722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:21.880722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting Lyndon factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen, Jamie Simpson, W. F. Smyth","submitted_at":"2017-01-04T08:19:56Z","abstract_excerpt":"In this paper, we determine the maximum number of distinct Lyndon factors that a word of length $n$ can contain. We also derive formulas for the expected total number of Lyndon factors in a word of length $n$ on an alphabet of size $\\sigma$, as well as the expected number of distinct Lyndon factors in such a word. The minimum number of distinct Lyndon factors in a word of length $n$ is $1$ and the minimum total number is $n$, with both bounds being achieved by $x^n$ where $x$ is a letter. A more interesting question to ask is what is the minimum number of distinct Lyndon factors in a Lyndon wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00928","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":"1701.00928","created_at":"2026-05-18T00:53:21.880796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.00928v1","created_at":"2026-05-18T00:53:21.880796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00928","created_at":"2026-05-18T00:53:21.880796+00:00"},{"alias_kind":"pith_short_12","alias_value":"HEVJNO5NSEW3","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HEVJNO5NSEW3RVTD","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HEVJNO5N","created_at":"2026-05-18T12:31:18.294218+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/HEVJNO5NSEW3RVTDCDTEV3O5UK","json":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK.json","graph_json":"https://pith.science/api/pith-number/HEVJNO5NSEW3RVTDCDTEV3O5UK/graph.json","events_json":"https://pith.science/api/pith-number/HEVJNO5NSEW3RVTDCDTEV3O5UK/events.json","paper":"https://pith.science/paper/HEVJNO5N"},"agent_actions":{"view_html":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK","download_json":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK.json","view_paper":"https://pith.science/paper/HEVJNO5N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.00928&json=true","fetch_graph":"https://pith.science/api/pith-number/HEVJNO5NSEW3RVTDCDTEV3O5UK/graph.json","fetch_events":"https://pith.science/api/pith-number/HEVJNO5NSEW3RVTDCDTEV3O5UK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK/action/storage_attestation","attest_author":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK/action/author_attestation","sign_citation":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK/action/citation_signature","submit_replication":"https://pith.science/pith/HEVJNO5NSEW3RVTDCDTEV3O5UK/action/replication_record"}},"created_at":"2026-05-18T00:53:21.880796+00:00","updated_at":"2026-05-18T00:53:21.880796+00:00"}