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Fulman independently found the limiting proportion of cyclic matrices in general linear groups over a finite field of fixed order q as the dimension n approaches infinity, namely $(1-q^{-5}) \\prod_{i=3}^\\infty (1-q^{-i}) = 1 - q^{-3} + O(q^{-4}).$ We study cyclic matrices in a maximal "},"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":"1105.4078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-20T13:13:28Z","cross_cats_sorted":[],"title_canon_sha256":"b03ba9c1d2106cab858ae07705d3deb7c045c4222f83e3cd99c6f4af2bb9a270","abstract_canon_sha256":"d6e0052490a36a1040472bec38e9a5fd9495e2fd607c1a0d29572a76f9eb5dbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:43.021312Z","signature_b64":"zYpUenV7vaz/PheMfhC3/5uhKsB+r1Bq2XkwKgIhfuYLtPRA7WP9Q0u/FJAjcC9uMTD/kjoMtU9BfwmisJphAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"155eefa1f4eadeae58acb2f70741a9cb6466494f14d3a855668b4ec2016fd686","last_reissued_at":"2026-05-18T04:21:43.020651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:43.020651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proportions of Cyclic Matrices in Maximal Reducible Matrix Groups and Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Cheryl E. 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