{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YFYRUPJWBJBQCGDRJTOMPNXJ2Q","short_pith_number":"pith:YFYRUPJW","schema_version":"1.0","canonical_sha256":"c1711a3d360a430118714cdcc7b6e9d402828b24836225f1596f2f30db02d16f","source":{"kind":"arxiv","id":"1902.02333","version":1},"attestation_state":"computed","paper":{"title":"Unary Patterns of Size Four with Morphic Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","cs.LO"],"primary_cat":"math.CO","authors_text":"Kamellia Reshadi","submitted_at":"2019-02-05T15:05:29Z","abstract_excerpt":"We investigate the avoidability of unary patterns of size of four with morphic permutations. More precisely, we show that, for the positive integers $i,j,k$, the sizes of the alphabets over which a pattern $x \\pi ^ {i} (x) \\pi^{j}(x) \\pi^{k}(x)$ is avoidable are an interval of the integers (where $x$ is a word variable and $\\pi$ is a function variable with values in the set of all morphic permutations of the respective alphabets). We also show how to compute a good approximation of this interval. This continues the work of [Manea et al., 2015], where a complete characterisation of the avoidabi"},"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":"1902.02333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-05T15:05:29Z","cross_cats_sorted":["cs.FL","cs.LO"],"title_canon_sha256":"90a1b294c0c0cad300223cf4799ddefa47daf65a261dd5e0671791c6f6c88e1f","abstract_canon_sha256":"bcda2323155c889ee3702bfb9a3e6f21c85022f257112e9984e676da007875ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:40.669179Z","signature_b64":"Ov4ydPQh20Mk+eBbpPB3nIcRBq9R57G3enE7nfDJJuSmAklKJn99WMt9Jq15ornTiLc/V8EsV0r9OPJf5q8GDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1711a3d360a430118714cdcc7b6e9d402828b24836225f1596f2f30db02d16f","last_reissued_at":"2026-05-17T23:50:40.668771Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:40.668771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unary Patterns of Size Four with Morphic Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","cs.LO"],"primary_cat":"math.CO","authors_text":"Kamellia Reshadi","submitted_at":"2019-02-05T15:05:29Z","abstract_excerpt":"We investigate the avoidability of unary patterns of size of four with morphic permutations. More precisely, we show that, for the positive integers $i,j,k$, the sizes of the alphabets over which a pattern $x \\pi ^ {i} (x) \\pi^{j}(x) \\pi^{k}(x)$ is avoidable are an interval of the integers (where $x$ is a word variable and $\\pi$ is a function variable with values in the set of all morphic permutations of the respective alphabets). We also show how to compute a good approximation of this interval. This continues the work of [Manea et al., 2015], where a complete characterisation of the avoidabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02333","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":"1902.02333","created_at":"2026-05-17T23:50:40.668836+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.02333v1","created_at":"2026-05-17T23:50:40.668836+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02333","created_at":"2026-05-17T23:50:40.668836+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFYRUPJWBJBQ","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFYRUPJWBJBQCGDR","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFYRUPJW","created_at":"2026-05-18T12:33:33.725879+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/YFYRUPJWBJBQCGDRJTOMPNXJ2Q","json":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q.json","graph_json":"https://pith.science/api/pith-number/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/graph.json","events_json":"https://pith.science/api/pith-number/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/events.json","paper":"https://pith.science/paper/YFYRUPJW"},"agent_actions":{"view_html":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q","download_json":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q.json","view_paper":"https://pith.science/paper/YFYRUPJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.02333&json=true","fetch_graph":"https://pith.science/api/pith-number/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/action/storage_attestation","attest_author":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/action/author_attestation","sign_citation":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/action/citation_signature","submit_replication":"https://pith.science/pith/YFYRUPJWBJBQCGDRJTOMPNXJ2Q/action/replication_record"}},"created_at":"2026-05-17T23:50:40.668836+00:00","updated_at":"2026-05-17T23:50:40.668836+00:00"}