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The non-existence of certain finite linear spaces

✍ Scribed by D. R. Stinson

Publisher
Springer
Year
1983
Tongue
English
Weight
272 KB
Volume
13
Category
Article
ISSN
0046-5755

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✦ Synopsis

We study the existence of finite linear spaces with v points and n 2 -}-n + 2 lines, where n 2 + 1 ~< v ~< n 2 + n + 1. For n ~> 3, there is only one such linear space; it has ten points and fourteen lines.

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Existence of certain skew room frames wi
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## Abstract It is shown that for any even integer __n__ β‰₯ 16 and for some __b__ β‰₯ 1, there exists a skew Room frame of type 2^__a__^ 4^__b__^ with __n__ = 2__a__ + 4__b__. As an application, we show that for any integer __v__ ≑ 1,4 (mod 12), there exists a weakly 3‐chromatic linear space with all l