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Combinatorics of Partial Geometries and Generalized Quadrangles

  • Conference paper
Higher Combinatorics

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 31))

Abstract

A finite partial geometry [17] is an incidence structure S=(P,B,I), with a symmetric incidence relation satisfying the following axioms

  1. (i)

    each point is incident with 1+t lines (t⩾1)and two distinct points are incident with at most one line;

  2. (ii)

    each line is incident with 1+s points (s⩾1) and two distinct lines are incident with at most one point;

  3. (iii)

    if x is a point and L is a line not incident with x, then there are exactly α (α ⩾1) points x1 ,x2 ,…,xα and α lines L1 ,L2 ,…, Lα such that xILi Ixi IL, i=1,2,…,α.

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Authors and Affiliations

  1. State University of Ghent, The Netherlands

    J. A. Thas

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  1. J. A. Thas
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Editors and Affiliations

  1. Fachbereich Mathematik, Freie Universität Berlin, Königin-Luise-Strasse 24/26, D-1000, Berlin 33, Germany

    Martin Aigner

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© 1977 D. Reidel Publishing Company, Dordrecht-Holland

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Thas, J.A. (1977). Combinatorics of Partial Geometries and Generalized Quadrangles. In: Aigner, M. (eds) Higher Combinatorics. NATO Advanced Study Institutes Series, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1220-1_11

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  • DOI: https://doi.org/10.1007/978-94-010-1220-1_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1222-5

  • Online ISBN: 978-94-010-1220-1

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