The Complement of Binary Klein Quadric as a Combinatorial Grassmannian

Metod Saniga
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Metod Saniga: Institute for Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10, A-1040 Vienna, Austria

Mathematics, 2015, vol. 3, issue 2, 1-6

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).

Keywords: combinatorial Grassmannian; binary Klein quadric; Conwell heptad; three-qubit Pauli group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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