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Span-Symmetric Generalized Quadrangles

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The Geometric Vein

Abstract

A generalized quadrangle (GQ) of order (s,t) is a point-line incidence geometry S = (P,L,I) with pointset P, lineset L and incidence relation I satisfying the following:

  1. (1)

    Two points are incident with at most one line in common.

  2. (2)

    If x ∈ P, L ∈ L, and x I L (i.e. x is not incident with L),there is a unique pair (y,M)∈ P × L for which x I M I y I L.

  3. (3)

    Each point (respectively, line) is incident with 1 + t lines (respectively, 1 + s points).

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References

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Author information

Authors and Affiliations

  1. Miami University, Oxford, Ohio, 45056, USA

    Stanley E. Payne

Authors
  1. Stanley E. Payne
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, M5S 1A1, Canada

    Chandler Davis  & F. A. Sherk  & 

  2. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Branko Grünbaum

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© 1981 Springer-Verlag New York Inc.

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Payne, S.E. (1981). Span-Symmetric Generalized Quadrangles. In: Davis, C., Grünbaum, B., Sherk, F.A. (eds) The Geometric Vein. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5648-9_15

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  • DOI: https://doi.org/10.1007/978-1-4612-5648-9_15

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-5650-2

  • Online ISBN: 978-1-4612-5648-9

  • eBook Packages: Springer Book Archive

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