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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Switching sets in $ {\rm PG}(3,\,q)$


Authors: A. Bruen and R. Silverman
Journal: Proc. Amer. Math. Soc. 43 (1974), 176-180
MSC: Primary 50D30; Secondary 05BXX
DOI: https://doi.org/10.1090/S0002-9939-1974-0333946-8
MathSciNet review: 0333946
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Abstract: In this note, we are mainly concerned with partial spreads $ U,V$ of $ PG(3,q)$ which cover the same points and have no line in common. Setting $ \vert U\vert = \vert V\vert = t$, we show that if $ t > q + 1$ then $ t \geqq \max (q + 2,2q - 2)$. Certain applications of this result to (0, 1) matrices and to translation planes are then discussed.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0333946-8
Keywords: Partial spread, replaceable net, embeddable net, regulus, double-six, translation plane, $ (0,1)$ matrix
Article copyright: © Copyright 1974 American Mathematical Society