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Adjoints of a Geometry

Published online by Cambridge University Press:  20 November 2018

Alan L. C. Cheung
Alan L. C. Cheung*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 363 - 365
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Crapo, H. H., Orthogonal Representations of Combinatorial Geometries in Atti del Convegno di Geometria Combinatoria e sue Applicazione, (Perugia, 11-17 Settembre 1970).Google Scholar
2. Crapo, H. H. and Rota, G.-C., On the Foundation of Combinatorial Theory: Combinatorial Geometries (M.I.T. Press, Cambridge, Mass., 1970).Google Scholar
3. Higgs, D. A., A lattice order for the set of all matroids on a set , Canadian Math. Bull., V.9. p. 684-685, (1966).Google Scholar