Skip to main content
SpringerLink
Log in

On Small and Large Hyperplanes of DW(5, q)

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

We determine lower and upper bounds for the size of a hyperplane of the dual polar space DW(5, q). In some cases, we also determine all hyperplanes attaining these bounds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Cooperstein, B. N., Pasini, A.: The non-existence of ovoids of the dual polar space DW(5, q), J. Combin. Theory Ser. A 104, 351–364 (2004)

    Google Scholar 

  • De Bruyn, B.: Near polygons. Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006

  • De Bruyn, B., Pralle, H.: The hyperplanes of DH(5, q2). Forum Math. to appear

  • De Bruyn B., Pralle, H.: The exceptional hyperplanes of DH(5, 4), Eur. J. Combin. 28, 1412–1418 (2007)

    Google Scholar 

  • De Bruyn, B., Vandecasteele, P.: The distance-2-sets of the slim dense near hexagons, Ann. Comb. 10, 179–196 (2006)

    Google Scholar 

  • Pasechnik, D.: Extending dual polar spaces of rank at least 3, J. Combin. Theory Ser. A 72, 232–242 (1995)

    Google Scholar 

  • Pasini, A., Shpectorov, S.: Uniform hyperplanes of finite dual polar spaces of rank 3, J. Combin. Theory Ser. A 94, 276–288 (2001)

    Google Scholar 

  • Payne, S.E., Thas, J.A.: Finite Generalized Quadrangles. Research Notes in Mathematics, vol. 110, Pitman, Boston, 1984

  • Pralle, H.: Hyperplanes of dual polar spaces of rank 3 with no subquadrangular quad, Adv. Geom. 2, 107–122 (2002)

    Google Scholar 

  • Pralle, H.: The hyperplanes of DW(5, 2), Exp. Math. 14, 373–384 (2005)

    Google Scholar 

  • Ronan, R.: Embeddings and hyperplanes of discrete geometries, Eur. J. Combin. 8, 179–185 (1987)

    Google Scholar 

  • Shult, E.E.: Generalized hexagons as geometric hyperplanes of near hexagons. In: Liebeck, M., Saxl, J. (eds.) Groups, Combinatorics and Geometry, pp. 229–239, Cambridge University Press, 1992

  • Shult, E.E., Yanushka, A.: Near n-gons and line systems, Geom. Dedicata 9, 1–72 (1980)

    Google Scholar 

  • Tits, J.: Buildings of Spherical Type and Finite BN-pairs. Lecture Notes in Mathematics, vol. 386, Springer, Berlin, 1974

Download references

Author information

Authors and Affiliations

  1. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 (S22), 9000, Gent, Belgium

    B. De Bruyn

  2. Inst. Computational Mathematics, Technische Universität Braunschweig, Pockelsstr. 14, 38106, Braunschweig, Germany

    H. Pralle

Authors
  1. B. De Bruyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Pralle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. De Bruyn.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruyn, B.D., Pralle, H. On Small and Large Hyperplanes of DW(5, q). Graphs and Combinatorics 23, 367–380 (2007). https://doi.org/10.1007/s00373-007-0730-3

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-007-0730-3

Keywords

Search

Navigation