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The Complement of Binary Klein Quadric as a Combinatorial Grassmannian

Author

Listed:
  • Metod Saniga

    (Institute for Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10, A-1040 Vienna, Austria
    Astronomical Institute, Slovak Academy of Sciences, SK-05960 Tatranská Lomnica, Slovak Republic)

Abstract

Given a hyperbolic quadric of PG(5, 2), there are 28 points off this quadric and 56 lines skew to it. It is shown that the (286; 563)-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type G2(8). It is also pointed out that a set of seven points of G2(8) whose labels share a mark corresponds to a Conwell heptad of PG(5, 2). Gradual removal of Conwell heptads from the (286; 563)-configuration yields a nested sequence of binomial configurations identical with part of that found to be associated with Cayley-Dickson algebras (arXiv:1405.6888).

Suggested Citation

  • Metod Saniga, 2015. "The Complement of Binary Klein Quadric as a Combinatorial Grassmannian," Mathematics, MDPI, vol. 3(2), pages 1-6, June.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:2:p:481-486:d:50849
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