Geodesic
Transversal lattices
The electronic journal of combinatorics, Tome 15 (2008)
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A flat of a matroid is cyclic if it is a union of circuits; such flats form a lattice under inclusion and, up to isomorphism, all lattices can be obtained this way. A lattice is a Tr-lattice if all matroids whose lattices of cyclic flats are isomorphic to it are transversal. We investigate some sufficient conditions for a lattice to be a Tr-lattice; a corollary is that distributive lattices of dimension at most two are Tr-lattices. We give a necessary condition: each element in a Tr-lattice has at most two covers. We also give constructions that produce new Tr-lattices from known Tr-lattices.
DOI : 10.37236/739
Classification : 05B35
Mots-clés : cyclic flat of a matroid, Tr-lattices, transversal matroids, distributive lattices, covers 
@article{10_37236_739,
     author = {Joseph E. Bonin},
     title = {Transversal lattices},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/739},
     zbl = {1159.05012},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/739/}
}
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Joseph E. Bonin. Transversal lattices. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/739

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