Abstract
We study to which extent all pairs of opposite vertices of self-opposite type determine a given building. We provide complete answers in the case of buildings related to projective spaces, to polar spaces and the exceptional buildings, but for the latter we restrict to the vertices whose Grassmannian defines a parapolar space of point diameter 3. Some results about non-self opposite types for buildings of types \({\mathsf{A}_n}\), \({\mathsf{D}_m}\) (m odd), and \({\mathsf{E}_6}\) are also provided.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.
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Kasikova, A., Van Maldeghem, H. Vertex opposition in spherical buildings. Des. Codes Cryptogr. 68, 285–318 (2013). https://doi.org/10.1007/s10623-012-9643-0
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DOI: https://doi.org/10.1007/s10623-012-9643-0