Analysis reveals that symplectic spaces and certain bilinear forms lack the Ramsey property, suggesting new insights.
We study the Ramsey property for vector spaces over finite fields with bilinear forms. We prove that symplectic spaces over finite fields do not have the Ramsey property. We also describe vector spaces with skew symmetric bilinear forms and radicals of finite codimension, where the Ramsey property does not hold. Some direct connections with generalized affine spaces are given.
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Иванов et al. (2025) studied this question.
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