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We present a method of compacting laminar presentations, characterize the class of laminar matroids by their excluded minors, present a way to construct all laminar matroids using basic operations, and compare the class of laminar matroids"},"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":"1606.08354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-27T16:26:27Z","cross_cats_sorted":[],"title_canon_sha256":"fee83f65ccb371e1dd20b56390c173700b94cc8054ea72b1a61193b10f1607b7","abstract_canon_sha256":"d47bab7527254d6605e2e77b1b712a174de33dad3ffcee2d968c3570f47c01a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:52.296101Z","signature_b64":"UgUfRsdyGchBUBuW4UAmd+ueUjitH5C2l91qYmOZjXDL9j3eB3yrYDlKR46jraNFkEw5rNjZ4NI08QYCG4ovCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0214dfeb75b2faa8e3307607dd7ec325db04df741ac45e4d7daa8bc3574e4e74","last_reissued_at":"2026-05-18T01:11:52.295739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:52.295739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Laminar Matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"James Oxley, Tara Fife","submitted_at":"2016-06-27T16:26:27Z","abstract_excerpt":"A laminar family is a collection $\\mathscr{A}$ of subsets of a set $E$ such that, for any two intersecting sets, one is contained in the other. 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