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Proceedings of the American Mathematical Society

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Geometrical realization of combinatorial geometries

Author: J. H. Mason
Journal: Proc. Amer. Math. Soc. 30 (1971), 15-21
MSC: Primary 05B35
MathSciNet review: 0309769
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Abstract: A method of depicting combinatorial geometries geometrically is used to construct examples of small combinatorial geometries which arise as subsets of a vector space over division rings restricted by their characteristic.

References [Enhancements On Off] (What's this?)

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  • [3] A. W. Ingleton, A note on independence functions and rank, J. London Math. Soc. 34 (1959), 49–56. MR 0101848
  • [4] T. Lazarson, The representation problem for independence functions, J. London Math. Soc. 33 (1958), 21–25. MR 0098701
  • [5] S. Mac Lane, Some intepretations of abstract linear dependence in terms of projective geometry, Amer. J. Math. 28 (1937), 22-32.
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Keywords: Combinatorial geometry, representation, vector space, division ring, rank, circuit, Euclidean space, nonrepresentable geometry
Article copyright: © Copyright 1971 American Mathematical Society