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Mathematics 2015, 3(2), 481-486; doi:10.3390/math3020481

The Complement of Binary Klein Quadric as a Combinatorial Grassmannian

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
Received: 9 May 2015 / Accepted: 5 June 2015 / Published: 8 June 2015
(This article belongs to the Special Issue Mathematical physics)
View Full-Text   |   Download PDF [172 KB, uploaded 8 June 2015]

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). 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Saniga, M. The Complement of Binary Klein Quadric as a Combinatorial Grassmannian. Mathematics 2015, 3, 481-486.

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