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The characterization problem for designs with the parameters of AGd(n, q)

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Abstract

We start a new characterization of the geometric 2-design AG d (n,q) among all simple 2-designs with the same parameters by handling the cases d ∈ {1,2,3,n — 2}. For d ≠ 1, our characterization is in terms of line sizes, and for d = 1 in terms of the number of affine hyperplanes. We also show that the number of non-isomorphic resolvable designs with the parameters of AG1(n,q) grows exponentially with linear growth of n.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Diskrete Mathematik Optimierung und Operations Research, Universität Augsburg, 86135, Augsburg, Germany

    Dieter Jungnickel

  2. Mathematisches Institut, Universität Gießen, Arndtstrasse 2, 35392, Gießen, Germany

    Klaus Metsch

  3. Department of Mathematics, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium

    Klaus Metsch

Authors
  1. Dieter Jungnickel
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  2. Klaus Metsch
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Correspondence to Dieter Jungnickel.

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In memoriam Hanfried Lenz

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Jungnickel, D., Metsch, K. The characterization problem for designs with the parameters of AGd(n, q). Combinatorica 36, 513–535 (2016). https://doi.org/10.1007/s00493-014-3212-2

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  • DOI: https://doi.org/10.1007/s00493-014-3212-2

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