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arXiv · 2509.14798

Bijection Between Point-Hyperplane Anti-Flags of $V(n, 2)$ and Non-Singular Points of $O^+(2n, 2)$

Ferdinand Ihringer·Antonio Pasini
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Abstract

We give a bijection between the point-hyperplane antiflags of $V(n, 2)$ and the nonsingular points of $V(2n, \allowbreak 2)$ with respect to a hyperbolic quadric. With the help of this bijection, we give a description of the strongly regular graph $NO^+_{2n}(2)$ in $V(2n, 2)$. We also describe a graph with respect to a hyperbolic quadric in $V(2n, 2)$ that was recently defined by Stanley and Takeda in $V(n, 2)$. Similarly, we give a bijection between the point-hyperplane antiflags of $V(n, 3)$ and the nonsingular points of one type in $V(2n, 3)$ with respect to a hyperbolic quadric.

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Ferdinand Ihringer, Antonio Pasini. 2025-09-18. Bijection Between Point-Hyperplane Anti-Flags of $V(n, 2)$ and Non-Singular Points of $O^+(2n, 2)$. https://arxiv.org/abs/2509.14798

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