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Finite affine planes in projective spaces

Joseph Thas (UGent) and Hendrik Van Maldeghem (UGent)
(2017) COMBINATORICA. 37(2). p.283-311
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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.
Keywords
Finite geometries, Block designs, Desarguesian and Pappian geometries, Incidence structures imbeddable into projective geometries, Affine and projective planes, Combinatorial structures in finite projective spaces

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Please use this url to cite or link to this publication:

MLA
Thas, Joseph, and Hendrik Van Maldeghem. “Finite Affine Planes in Projective Spaces.” COMBINATORICA 37.2 (2017): 283–311. Print.
APA
Thas, J., & Van Maldeghem, H. (2017). Finite affine planes in projective spaces. COMBINATORICA, 37(2), 283–311.
Chicago author-date
Thas, Joseph, and Hendrik Van Maldeghem. 2017. “Finite Affine Planes in Projective Spaces.” Combinatorica 37 (2): 283–311.
Chicago author-date (all authors)
Thas, Joseph, and Hendrik Van Maldeghem. 2017. “Finite Affine Planes in Projective Spaces.” Combinatorica 37 (2): 283–311.
Vancouver
1.
Thas J, Van Maldeghem H. Finite affine planes in projective spaces. COMBINATORICA. 2017;37(2):283–311.
IEEE
[1]
J. Thas and H. Van Maldeghem, “Finite affine planes in projective spaces,” COMBINATORICA, vol. 37, no. 2, pp. 283–311, 2017.
@article{8549998,
  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.},
  author       = {Thas, Joseph and Van Maldeghem, Hendrik},
  issn         = {0209-9683},
  journal      = {COMBINATORICA},
  keywords     = {Finite geometries,Block designs,Desarguesian and Pappian geometries,Incidence structures imbeddable into projective geometries,Affine and projective planes,Combinatorial structures in finite projective spaces},
  language     = {eng},
  number       = {2},
  pages        = {283--311},
  title        = {Finite affine planes in projective spaces},
  url          = {http://dx.doi.org/10.1007/s00493-014-3179-z},
  volume       = {37},
  year         = {2017},
}

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