{"paper":{"title":"Generalized 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":"2018-01-21T19:22:42Z","abstract_excerpt":"Nested matroids were introduced by Crapo in 1965 and have appeared frequently in the literature since then. A flat of a matroid $M$ is Hamiltonian if it has a spanning circuit. A matroid $M$ is nested if and only if its Hamiltonian flats form a chain under inclusion; $M$ is laminar if and only if, for every $1$-element independent set $X$, the Hamiltonian flats of $M$ containing $X$ form a chain under inclusion. We generalize these notions to define the classes of $k$-closure-laminar and $k$-laminar matroids. This paper focuses on structural properties of these classes noting that, while the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06882","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"}