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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.14798 |
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| _version_ | 1866911583264833536 |
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| author | Ihringer, Ferdinand Pasini, Antonio |
| author_facet | Ihringer, Ferdinand Pasini, Antonio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bijection Between Point-Hyperplane Anti-Flags of $V(n, 2)$ and Non-Singular Points of $O^+(2n, 2)$ Ihringer, Ferdinand Pasini, Antonio Combinatorics 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. |
| title | Bijection Between Point-Hyperplane Anti-Flags of $V(n, 2)$ and Non-Singular Points of $O^+(2n, 2)$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.14798 |