Geodesic
Adjoints of a Geometry
Canadian mathematical bulletin, Tome 17 (1974) no. 3, pp. 363-365

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DOI

To give a geometric interpretation to the inverted incidence relation between the flats of a geometry has for years been a tempting idea in combinatorial geometries [1]. If G is a geometric lattice, the inverted lattice G' is not necessarily geometric. 
Cheung, Alan L. C. Adjoints of a Geometry. Canadian mathematical bulletin, Tome 17 (1974) no. 3, pp. 363-365. doi: 10.4153/CMB-1974-066-5
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     author = {Cheung, Alan L. C.},
     title = {Adjoints of a {Geometry}},
     journal = {Canadian mathematical bulletin},
     pages = {363--365},
     year = {1974},
     volume = {17},
     number = {3},
     doi = {10.4153/CMB-1974-066-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-066-5/}
}
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