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Article Dans Une Revue Mathematics Année : 2015

The Complement of Binary Klein Quadric as a Combinatorial Grassmannian

Résumé

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 $(28_6, 56_3)$-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type $G_2(8)$. It is also pointed out that a set of seven points of $G_2(8)$ whose labels share a mark corresponds to a Conwell heptad of PG(5, 2). Gradual removal of Conwell heptads from the $(28_6, 56_3)$-configuration yields a nested sequence of binomial configurations identical with part of that found to be associated with Cayley-Dickson algebras (arXiv:1405.6888).
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Dates et versions

hal-01064747 , version 1 (17-09-2014)

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  • HAL Id : hal-01064747 , version 1

Citer

Metod Saniga. The Complement of Binary Klein Quadric as a Combinatorial Grassmannian. Mathematics , 2015, 3 (2), pp.481-486. ⟨hal-01064747⟩

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