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Open AccessLetter

The Complement of Binary Klein Quadric as a Combinatorial Grassmannian

by 1,2
1
Institute for Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10, A-1040 Vienna, Austria
2
Astronomical Institute, Slovak Academy of Sciences, SK-05960 Tatranská Lomnica, Slovak Republic 
Academic Editor: Palle E.T. Jorgensen
Mathematics 2015, 3(2), 481-486; https://doi.org/10.3390/math3020481
Received: 9 May 2015 / Accepted: 5 June 2015 / Published: 8 June 2015
(This article belongs to the Special Issue Mathematical physics)
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). View Full-Text
Keywords: combinatorial Grassmannian; binary Klein quadric; Conwell heptad; three-qubit Pauli group combinatorial Grassmannian; binary Klein quadric; Conwell heptad; three-qubit Pauli group
MDPI and ACS Style

Saniga, M. The Complement of Binary Klein Quadric as a Combinatorial Grassmannian. Mathematics 2015, 3, 481-486. https://doi.org/10.3390/math3020481

AMA Style

Saniga M. The Complement of Binary Klein Quadric as a Combinatorial Grassmannian. Mathematics. 2015; 3(2):481-486. https://doi.org/10.3390/math3020481

Chicago/Turabian Style

Saniga, Metod. 2015. "The Complement of Binary Klein Quadric as a Combinatorial Grassmannian" Mathematics 3, no. 2: 481-486. https://doi.org/10.3390/math3020481

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