A Note on Planar and Dismantlable Lattices
classification
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keywords
latticerank-connecteddismantlableinterval-connectedplanaradmissiblecohen-macaulayexample
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It is shown that any finite, rank-connected, dismantlable lattice is lexicographically shellable (hence Cohen-Macaulay). A ranked, interval-connected lattice is shown to be rank-connected, but a rank-connected lattice need not be interval-connected. An example of a planar, rank-connected lattice that is not admissible is given.
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