Sets of Disjoint Lines in PG(3, q)
1967 ◽
Vol 19
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pp. 273-280
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Keyword(s):
Let ∑ be a projective space PG(3, q) of dimension 3 and finite order q. Then ∑ contains (q + 1)(q2 + 1) points and an equal number of planes, and (q2 + 1) (q2 + q + 1) lines. It will be convenient to consider lines and planes as sets of points and to treat the incidence relation as set inclusion. Each plane contains q2 + q + 1 points and an equal number of lines. Each line contains q + 1 points and is contained in an equal number of planes. Each point is contained in q2 + q + 1 planes and an equal number of lines.A spread of lines of ∑ is a set of q2 + 1 lines of ∑ which are pairwise disjoint, or skew; it can also be defined as a set of lines such that each point (or each plane) is incident with exactly one of the lines.
1969 ◽
Vol 12
(6)
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pp. 801-803
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1990 ◽
Vol 108
(1)
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pp. 7-19
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2014 ◽
Vol 51
(4)
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pp. 547-555
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2007 ◽
Vol 7
(3)
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pp. 239-254
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Keyword(s):
Keyword(s):
Keyword(s):
2020 ◽
Vol 17
(5)
◽
pp. 744-747
1968 ◽
Vol 19
(6)
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pp. 1457-1457
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