Ovoid (polar space)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the field of combinatorics, a polar space of rank n (n 3), or projective index n 1, consists of a set P, conventionally the set of points, together with certain subsets of P, called subspaces, that satisfy these axioms : Every subspace, together with its own subspaces, is isomorphic with a partial geometry PG(d,q) with 1 d (n 1) and q a prime power. By definition, for each subspace the corresponding d is its dimension. The intersection of two subspa...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the field of combinatorics, a polar space of rank n (n 3), or projective index n 1, consists of a set P, conventionally the set of points, together with certain subsets of P, called subspaces, that satisfy these axioms : Every subspace, together with its own subspaces, is isomorphic with a partial geometry PG(d,q) with 1 d (n 1) and q a prime power. By definition, for each subspace the corresponding d is its dimension. The intersection of two subspaces is always a subspace. For each point p not in a subspace A of dimension of n 1, there is a unique subspace B of dimension n 1 such that A B is (n 2)-dimensional. The points in A B are exactly the points of A that are in a common subspace of dimension 1 with p. There are at least two disjoint subspaces of dimension n 1. A polar space of rank two is a generalized quadrangle.
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