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<p>We give a bijection between the point-hyperplane antiflags of <i>V</i>(<i>n</i>,&#xa0;2) and the nonsingular points of <i>V</i>(2<i>n</i>,&#xa0;2) with respect to a hyperbolic quadric. With the help of this bijection, we give a description of the strongly regular graph <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(NO^+_{2n}(2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <msubsup> <mi>O</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> <mo>+</mo> </msubsup> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> in <i>V</i>(2<i>n</i>,&#xa0;2). We also describe a graph with respect to a hyperbolic quadric in <i>V</i>(2<i>n</i>,&#xa0;2) that was recently defined by Stanley and Takeda in <i>V</i>(<i>n</i>,&#xa0;2). Similarly, we give a bijection between the point-hyperplane antiflags of <i>V</i>(<i>n</i>,&#xa0;3) and the nonsingular points of one type in <i>V</i>(2<i>n</i>,&#xa0;3) with respect to a hyperbolic quadric.</p>

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Bijection between point-hyperplane antiflags of V(n, 2) and nonsingular points of \(O^+(2n, 2)\)

  • 期刊论文

  • 发表日期：

    2026年5月3日

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  • Ferdinand Ihringer,
  • Antonio Pasini

摘要

We give a bijection between the point-hyperplane antiflags of V(n, 2) and the nonsingular points of V(2n, 2) with respect to a hyperbolic quadric. With the help of this bijection, we give a description of the strongly regular graph \(NO^+_{2n}(2)\) N O 2 n + ( 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.