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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 second class is always minor-closed, the first is if and only if k≤3. The main results are excluded-minor characterizations of the classes of 2-laminar and 2-closure-laminar matroids.

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European Journal of Combinatorics

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