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A combinatorial characterization of geometric spreads

✍ Scribed by Albrecht Beutelspacher

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
241 KB
Volume
97
Category
Article
ISSN
0012-365X

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✦ Synopsis

Beutelspacher

A., A combinatorial characterization of geometric spreads, Discrete Mathematics 97 (1991) 59-62.

A t-spread in a projective space P = PG(d, q) is a set of t-dimensional subspaces which partitions the point set of P. A t-spread S is called geometric if it induces a spread in any (2t + I)-dimensional subspace containing at least two elements of S. In this note we characterize the geometric t-spreads S among all partial spreads in the first nontrivial case PG(3t + 2, q) by the property that any subspace of dimension 3t contains at least one element of S. This is the first instance of a combinatorial characterization of geometric spreads.

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