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On the type of partial t-spreads in finite projective spaces

✍ Scribed by Albrecht Beutelspacher; Franco Eugeni

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
967 KB
Volume
54
Category
Article
ISSN
0012-365X

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✦ Synopsis

A partial t-spread in a projective space P is a set of mutually skew t-dimensional subspaces of P. In this paper, we deal with the question, how many elements of a partial spread Sf can be contained in a given d-dimensional subspace of P. Our main results run as follows. If any d-dimensional subspace of P contains at least one element of 9', then the dimension of P has the upper bound d-l+(d/t). The same conclusion holds, if no d-dimensional subspace contains precisely one element of 9'. If any d-dimensional subspace has the same number m > 0 of elements of 5e, then So is necessarily a total t-spread. Finally, the 'type' of the so-called geometric t-spreads is determined explicitely.

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