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Ramsey property for spaces with bilinear forms (2503.08312v1)
Published 11 Mar 2025 in math.LO and math.CO
Abstract: 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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