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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Geometrical realization of combinatorial geometries
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by J. H. Mason PDF
Proc. Amer. Math. Soc. 30 (1971), 15-21 Request permission

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
    H. H. Crapo and G.-C. Rota, Combinatorial geometries, privately printed, December 1968. J. E. Blackburn, H. H. Crapo and D. A. Higgs, A catalogue of combinatorial geometries (unpublished).
  • A. W. Ingleton, A note on independence functions and rank, J. London Math. Soc. 34 (1959), 49–56. MR 101848, DOI 10.1112/jlms/s1-34.1.49
  • T. Lazarson, The representation problem for independence functions, J. London Math. Soc. 33 (1958), 21–25. MR 98701, DOI 10.1112/jlms/s1-33.1.21
  • S. Mac Lane, Some intepretations of abstract linear dependence in terms of projective geometry, Amer. J. Math. 28 (1937), 22-32. P. Vamös, Private communication via R. A. Brualdi, July 1969.
  • Hassler Whitney, On the Abstract Properties of Linear Dependence, Amer. J. Math. 57 (1935), no. 3, 509–533. MR 1507091, DOI 10.2307/2371182
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 30 (1971), 15-21
  • MSC: Primary 05B35
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0309769-X
  • MathSciNet review: 0309769