منابع مشابه
Quadric Veronesean Caps
In [2], a characterization theorem for Veronesean caps in PG(N,K), with K a skewfield, is provided. This result extends the theorem for the finite case proved in [7]. Although the statement of this theorem is correct, the proof given in [2] is incomplete, as some lemmas from [7] are proved using counting arguments and hence require a different approach in the infinite case. In this paper we use...
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A t-cover of a quadric Q is a set C of t-dimensional subspaces contained in Q such that every point of Q belongs to at least one element of C. We consider t-covers of the Klein quadric Q+(5, q). For t = 2 we show that a 2-cover has at least q2+q elements, and we give an exact description of the examples of this cardinality. For t = 1, we show that a 1-cover has at least q3+2q+1 elements, and we...
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This paper is concerned with constructing caps embedded in line Grassman-nians. In particular, we construct a cap of size q 3 + 2q 2 + 1 embedded in the Klein quadric of P G(5; q) for even q, and show that any cap maximally embedded in the Klein quadric which is larger than this one must have size equal to the theoretical upper bound, namely q 3 + 2q 2 + q + 2. It is not known if caps achieving...
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Given a hyperbolic quadric of PG(5, 2), there are 28 points off this quadric and 56 lines skew to it. It is shown that the (286, 563)-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type G2(8). It is also pointed out that a set of seven points of G2(8) whose labels share a mark corresponds to a Conwell heptad of PG(5, 2). Gradual removal of Conw...
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We discuss a unified approach to a class of geometric combinatorics incidence problems in two dimensions, of the Erdős distance type. The goal is obtaining the second moment estimate. That is, given a finite point set S in 2D, and a function f on S × S, find the upper bound for the number of solutions of the equation (1) f(p, p′) = f(q, q′) 6= 0, (p, p′, q, q′) ∈ S × S × S × S. E.g., f is the E...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2000
ISSN: 1370-1444
DOI: 10.36045/bbms/1103055715