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A family $\\mathcal{M}$ of maximal subgroups of $G$ is called `irredundant' if its intersection is not equal to the intersection of any proper subfamily. $\\mathcal{M}$ is called `maximal irredundant' if $\\mathcal{M}$ is irredundant and it is not properly contained in any other irredundant family. We denote by $\\mbox{Mindim}(G)$ the minimal size of a maximal irredundant family of $G$. In this paper we compute $\\mbox{Mindim}(G)$ when $G$ is the alternating group on $n$ letters."},"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":"1808.04387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-08-13T18:14:05Z","cross_cats_sorted":[],"title_canon_sha256":"d57e8608803e2a9a5a3a2641c09d52be26e12528e6a55ee16f4a18c897f75f3d","abstract_canon_sha256":"bcfb3c0ad97bb923c52a5a4984e49501a80e4085625a6d9e2147920c6097a464"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:03.608823Z","signature_b64":"rJdLyTLhXTjl9c1B98KaMhuJZT/xDhBR5qY6KG/Fc7mfmCbDiw013Ew5lEloJqSW/9vPUgfhWg6D6KwVJBOeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f157354502e606019151604c11164201e43769870b37fd763d45cd0b200b9747","last_reissued_at":"2026-05-17T23:49:03.608348Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:03.608348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal irredundant families of minimal size in the alternating group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini, Martino Garonzi","submitted_at":"2018-08-13T18:14:05Z","abstract_excerpt":"Let $G$ be a finite group. 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