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Research of the Erdős-Ko-Rado theorem based on symplectic spaces over finite fields. (Chinese. English summary) Zbl 1424.05281

Summary: In this paper, we study the Erdős-Ko-Rado (EKR) theorem for isotropic subspaces of the symplectic space over finite fields. We obtain an upper bound for the \(r\)-intersection of isotropic subspaces of type \((m, 0)\) in the symplectic spaces by investigating monotonicity of an upper bound function.

MSC:

05D05 Extremal set theory
05B25 Combinatorial aspects of finite geometries
05E15 Combinatorial aspects of groups and algebras (MSC2010)
51A50 Polar geometry, symplectic spaces, orthogonal spaces
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