Symmetric designs and geometroids


Aλ-setS in a symmetric 2-(v, k, λ) designΠ is a subset which every block meets in 0, 1 orλ points such that for any point ofS there is a unique block meetingS at that point only. Ovoids in three-dimensional projective spaces are examples ofλ-secs. It is shown that ifπ has aλ-set thenπ is a geometroid withv=λu 2+u+1 andk=λu+1, whereu≧λ−1. The cases whenu isλ−1,λ andλ+1 are investigated and some open problems discussed.

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McDonough, T.P., Mavron, V.C. Symmetric designs and geometroids. Combinatorica 9, 51–57 (1989).

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AMS Subject Classification (1985)

  • 51 E05
  • 05 B05
  • 05B25
  • 51 E20