Sui q-archi completi in piani non desarguesiani di ordine q dispari
Abstract
By a well know theorem of Segre [5] and G. Tallini [7], the q-arcs of the desarguesian plane
, are not complete.In [1],[2],[3] it is shown that this theorem cannot be extended to any non-desarguesian plane.In this paper, the following theorem is proved: Let
be a complete q-arc of a projective plane 𝜋 of order q. Denote by
the number of those points P of 𝜋 for which the number of tangents of
passing through P is j. Then
when
;
for
.
![PG(2,q)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/0b78f77ae85a50f0ced942e1148f80ae.png)
![ω](http://siba-ese.unile.it/plugins/generic/latexRender/cache/45bf03a575f6e81359314e906fb2bff3.png)
![e<sub>j</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/04db1970d8774e582788d7c7d6cab8ec.png)
![ω](http://siba-ese.unile.it/plugins/generic/latexRender/cache/45bf03a575f6e81359314e906fb2bff3.png)
![e_{\frac{q+1}{2}}≤ 4](http://siba-ese.unile.it/plugins/generic/latexRender/cache/01b6bd9ae5e9039b799df080687ee109.png)
![q>15](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8c3d6b6c92c9bd7b23b1ae2a5e63063a.png)
![e_{\frac{q+h}{2}}≤ 3](http://siba-ese.unile.it/plugins/generic/latexRender/cache/23f051a49231216abe2f8d989c64032a.png)
![h=3,5,7\ldots](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c5e9ece651d7795e229009436964f9db.png)
DOI Code:
10.1285/i15900932v3n1p149
Full Text: PDF