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Journal of Geometry

, Volume 108, Issue 3, pp 1083–1084 | Cite as

Hyper-reguli in PG(5,\(\varvec{q}\))

  • S. G. Barwick
  • Wen-Ai Jackson
Article

Abstract

A simple counting argument is used to show that for all q, an André hyper-regulus \({\mathbb {X}}\) in \(\mathrm{PG}(5,q)\) has exactly two switching sets. Moreover, there are exactly \(2(q^2+q+1)\) planes in \(\mathrm{PG}(5,q)\) that meet every plane of \({\mathbb {X}}\) in a point, namely the planes in the switching sets.

Keywords

Circle geometry covers hyper-reguli 

Mathematics Subject Classification

51E20 

References

  1. 1.
    Bruck, R.H.: Circle geometry in higher dimensions. II. Geom. Dedic. 2, 133–188 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ostrom, T.G.: Hyper-reguli. J. Geom. 48, 157–166 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Pomareda, R.: Hyper-reguli in projective space of dimension 5, Mostly Finite Geometries (1996), Lecture Notes in Pure and Appl. Math., vol. 190, pp. 379–381 (1997)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematical ScienceUniversity of AdelaideAdelaideAustralia

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