{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KL5HLVCUAVXQZ3ZI36ISJRIVDR","short_pith_number":"pith:KL5HLVCU","schema_version":"1.0","canonical_sha256":"52fa75d454056f0cef28df9124c5151c4dcf98c4f7197816647bcfebb100512a","source":{"kind":"arxiv","id":"1301.5104","version":1},"attestation_state":"computed","paper":{"title":"On a generalization of Abelian equivalence and complexity of infinite words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Aleksi Saarela, Juhani Karhumaki, Luca Q. Zamboni","submitted_at":"2013-01-22T08:27:59Z","abstract_excerpt":"In this paper we introduce and study a family of complexity functions of infinite words indexed by $k \\in \\ints ^+ \\cup {+\\infty}.$ Let $k \\in \\ints ^+ \\cup {+\\infty}$ and $A$ be a finite non-empty set. Two finite words $u$ and $v$ in $A^*$ are said to be $k$-Abelian equivalent if for all $x\\in A^*$ of length less than or equal to $k,$ the number of occurrences of $x$ in $u$ is equal to the number of occurrences of $x$ in $v.$ This defines a family of equivalence relations $\\thicksim_k$ on $A^*,$ bridging the gap between the usual notion of Abelian equivalence (when $k=1$) and equality (when $"},"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":"1301.5104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T08:27:59Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"66c5aaacc601a00777b6fb0f986b162c4307d37e0f8981022e77c309cd1c1e6b","abstract_canon_sha256":"07c436c8eb3063077d265f40bd620dd16539a74481173fd7be4c8414bee606e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:53.037311Z","signature_b64":"FcOLdJYkkDd1XhRdIrkLRY6o/ONExC+d+cNDe+4CmJIlQAE6l7LE9AQciQsQs6WZFpGjMo3ZwGOYy9B+tQ31Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52fa75d454056f0cef28df9124c5151c4dcf98c4f7197816647bcfebb100512a","last_reissued_at":"2026-05-18T03:35:53.036578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:53.036578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a generalization of Abelian equivalence and complexity of infinite words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Aleksi Saarela, Juhani Karhumaki, Luca Q. Zamboni","submitted_at":"2013-01-22T08:27:59Z","abstract_excerpt":"In this paper we introduce and study a family of complexity functions of infinite words indexed by $k \\in \\ints ^+ \\cup {+\\infty}.$ Let $k \\in \\ints ^+ \\cup {+\\infty}$ and $A$ be a finite non-empty set. Two finite words $u$ and $v$ in $A^*$ are said to be $k$-Abelian equivalent if for all $x\\in A^*$ of length less than or equal to $k,$ the number of occurrences of $x$ in $u$ is equal to the number of occurrences of $x$ in $v.$ This defines a family of equivalence relations $\\thicksim_k$ on $A^*,$ bridging the gap between the usual notion of Abelian equivalence (when $k=1$) and equality (when $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5104","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":"1301.5104","created_at":"2026-05-18T03:35:53.036701+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5104v1","created_at":"2026-05-18T03:35:53.036701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5104","created_at":"2026-05-18T03:35:53.036701+00:00"},{"alias_kind":"pith_short_12","alias_value":"KL5HLVCUAVXQ","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"KL5HLVCUAVXQZ3ZI","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"KL5HLVCU","created_at":"2026-05-18T12:27:51.066281+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/KL5HLVCUAVXQZ3ZI36ISJRIVDR","json":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR.json","graph_json":"https://pith.science/api/pith-number/KL5HLVCUAVXQZ3ZI36ISJRIVDR/graph.json","events_json":"https://pith.science/api/pith-number/KL5HLVCUAVXQZ3ZI36ISJRIVDR/events.json","paper":"https://pith.science/paper/KL5HLVCU"},"agent_actions":{"view_html":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR","download_json":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR.json","view_paper":"https://pith.science/paper/KL5HLVCU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5104&json=true","fetch_graph":"https://pith.science/api/pith-number/KL5HLVCUAVXQZ3ZI36ISJRIVDR/graph.json","fetch_events":"https://pith.science/api/pith-number/KL5HLVCUAVXQZ3ZI36ISJRIVDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR/action/storage_attestation","attest_author":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR/action/author_attestation","sign_citation":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR/action/citation_signature","submit_replication":"https://pith.science/pith/KL5HLVCUAVXQZ3ZI36ISJRIVDR/action/replication_record"}},"created_at":"2026-05-18T03:35:53.036701+00:00","updated_at":"2026-05-18T03:35:53.036701+00:00"}