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<p>We present a constructive procedure for finite geometries, in particular biplanes of order 9, based on structural invariants arising from the incidence matrix form. For the purpose to characterise these invariants we introduce the notion of biplane’s non-transversal vectors. These vectors enable significant reduction of the search space required for an explicit construction. We constructed multiple known biplanes, including those with large automorphism groups.</p>

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Biplane constructions by means of structural invariants

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Ivica Martinjak,
  • Matko Glunčić

摘要

We present a constructive procedure for finite geometries, in particular biplanes of order 9, based on structural invariants arising from the incidence matrix form. For the purpose to characterise these invariants we introduce the notion of biplane’s non-transversal vectors. These vectors enable significant reduction of the search space required for an explicit construction. We constructed multiple known biplanes, including those with large automorphism groups.