On classification of some finite linear spaces
We classified all finite linear spaces having property: for every pair L, L' of intersecting lines, and every point p not on either of these, there are L lines through p disjoint from both L and L', where the nonnegative number L is constant. This space will be denoted by (2i,0,L)-interlac...
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| Format: | Article |
| Language: | English |
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BİSKA Bilisim Company
2015-11-01
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| Series: | New Trends in Mathematical Sciences |
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| Online Access: | https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=3096 |
| Summary: | We classified all finite linear spaces having property: for every pair L, L' of
intersecting lines, and every point p not on either of these, there are L lines through
p disjoint from both L and L', where the nonnegative number L is constant. This
space will be denoted by (2i,0,L)-interlaced.
In the present paper, we will show that this property (with L arbitrary) essentially
characterizes the semia¢ ne planes with non-constant line size. For linear spaces with
constant line size, this property does not seem to be strong enough, but we derive
some necessary conditions on the parameters showing that examples will be hard
to find. |
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| ISSN: | 2147-5520 2147-5520 |