Finite affine planes in projective spaces

Abstract

We classify all representations of an arbitrary affine plane A of order q in a projective space PG(d,q) such that lines of A correspond with affine lines and/or plane q-arcs and such that for each plane q-arc which corresponds to a line L of A the plane of PG(d,q) spanned by the q-arc does not contain the image of any point off L of A.

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Correspondence to Joseph A. Thas.

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Thas, J.A., Van Maldeghem, H. Finite affine planes in projective spaces. Combinatorica 37, 283–311 (2017). https://doi.org/10.1007/s00493-014-3179-z

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Mathematics Subject Classification (2000)

  • 05B25
  • 05B05
  • 51A30
  • 51A45
  • 51E15
  • 51E20
  • 51B99