{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2SLJBOSTQYEG3U767I27OFSWMG","short_pith_number":"pith:2SLJBOST","schema_version":"1.0","canonical_sha256":"d49690ba5386086dd3fefa35f7165661828b507da5839448864a53961d70ca79","source":{"kind":"arxiv","id":"1307.3881","version":1},"attestation_state":"computed","paper":{"title":"On the matrix sequence $\\{\\Gamma(A^m)\\}_{m=1}^\\infty$ for a Boolean matrix $A$ whose digraph is linearly connected","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jihoon Choi, Suh-Ryung Kim","submitted_at":"2013-07-15T10:43:11Z","abstract_excerpt":"In this paper, we extend the results given by Park {\\em et al.} \\cite{ppk} by studying the convergence of the matrix sequence $\\{\\Gamma(A^m)\\}_{m=1}^\\infty$ for a matrix $A \\in \\mathcal{B}_n$ the digraph of which is linearly connected with an arbitrary number of strong components. In the process for generalization, we concretize ideas behind their arguments. We completely characterize $A$ for which $\\{\\Gamma(A^m)\\}_{m=1}^\\infty$ converges. Then we find its limit when all of the irreducible diagonal blocks are of order at least two. We go further to characterize $A$ for which the limit of $\\{\\G"},"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":"1307.3881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-15T10:43:11Z","cross_cats_sorted":[],"title_canon_sha256":"704e83d7dab6af6a9afaaa87cf58185632f1354530b74b3bdfc5eaa9b84a1a7c","abstract_canon_sha256":"10fb8b2914642ef0df33a8f835887d17ea4f61f056539749d3ea8b39534fb151"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:27.558334Z","signature_b64":"QV1Ateu8YkPDUnpjiuFqJ+l2i1U3SzaP2FIyniKZInJNY7QLNxENHOudEVdYVKKYALSRopXSlUiaV3B5vKhrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d49690ba5386086dd3fefa35f7165661828b507da5839448864a53961d70ca79","last_reissued_at":"2026-05-18T03:18:27.557703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:27.557703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the matrix sequence $\\{\\Gamma(A^m)\\}_{m=1}^\\infty$ for a Boolean matrix $A$ whose digraph is linearly connected","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jihoon Choi, Suh-Ryung Kim","submitted_at":"2013-07-15T10:43:11Z","abstract_excerpt":"In this paper, we extend the results given by Park {\\em et al.} \\cite{ppk} by studying the convergence of the matrix sequence $\\{\\Gamma(A^m)\\}_{m=1}^\\infty$ for a matrix $A \\in \\mathcal{B}_n$ the digraph of which is linearly connected with an arbitrary number of strong components. In the process for generalization, we concretize ideas behind their arguments. We completely characterize $A$ for which $\\{\\Gamma(A^m)\\}_{m=1}^\\infty$ converges. Then we find its limit when all of the irreducible diagonal blocks are of order at least two. We go further to characterize $A$ for which the limit of $\\{\\G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3881","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":"1307.3881","created_at":"2026-05-18T03:18:27.557794+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3881v1","created_at":"2026-05-18T03:18:27.557794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3881","created_at":"2026-05-18T03:18:27.557794+00:00"},{"alias_kind":"pith_short_12","alias_value":"2SLJBOSTQYEG","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"2SLJBOSTQYEG3U76","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"2SLJBOST","created_at":"2026-05-18T12:27:32.513160+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/2SLJBOSTQYEG3U767I27OFSWMG","json":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG.json","graph_json":"https://pith.science/api/pith-number/2SLJBOSTQYEG3U767I27OFSWMG/graph.json","events_json":"https://pith.science/api/pith-number/2SLJBOSTQYEG3U767I27OFSWMG/events.json","paper":"https://pith.science/paper/2SLJBOST"},"agent_actions":{"view_html":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG","download_json":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG.json","view_paper":"https://pith.science/paper/2SLJBOST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3881&json=true","fetch_graph":"https://pith.science/api/pith-number/2SLJBOSTQYEG3U767I27OFSWMG/graph.json","fetch_events":"https://pith.science/api/pith-number/2SLJBOSTQYEG3U767I27OFSWMG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG/action/storage_attestation","attest_author":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG/action/author_attestation","sign_citation":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG/action/citation_signature","submit_replication":"https://pith.science/pith/2SLJBOSTQYEG3U767I27OFSWMG/action/replication_record"}},"created_at":"2026-05-18T03:18:27.557794+00:00","updated_at":"2026-05-18T03:18:27.557794+00:00"}