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Independence in Combinatorial Geometries of Rank Three

Published online by Cambridge University Press:  20 November 2018

Japheth Hall Jr.
Japheth Hall Jr.*
Affiliation:
Stillman CollegeP.O. Box 1430, Tuscaloosa Alabama, 34501, U.S.A.
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The class of all combinatorial geometries of rank three shall coincide with the class of all pairs (V, S) such that V is a set and S is a collection of non-empty subsets of V such that each pair of distinct elements of V belong to exactly one member of S. (See [3].)

Consider a combinatorial geometry (V, S) of rank three.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 217 - 221
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bleicher, M. N. and Marczewski, E., Remarks on dependence relations and closure operators, Colloquium Mathematicum IX (1962), 209-211.Google Scholar
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3. Crapo-Rota, Combinatorial Geometries, MIT Press, 1970.Google Scholar
4. Hall, J. Jr., A condition for equality of cardinals of minimal generators under closure operators, Canad. Math. Bull. 14 (4), 1971.Google Scholar
5. Hall, J. Jr., The independence of certain axions of structures in sets, Proceedings of the Amer. Math. Soc. 31 (2) (1972), 317-325.Google Scholar
6. Hall, J. Jr., On the Theory of Structures in Sets, Dissertation Abstracts International XXXI (10), 1971.Google Scholar