Sui q-archi completi in piani non desarguesiani di ordine q dispari


By a well know theorem of Segre [5] and G. Tallini [7], the q-arcs of the desarguesian plane PG(2,q), 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 ω be a complete q-arc of a projective plane 𝜋 of order q. Denote by e<sub>j</sub> the number of those points P of 𝜋 for which the number of tangents of ω passing through P is j. Then e_{\frac{q+1}{2}}≤ 4 when q>15; e_{\frac{q+h}{2}}≤ 3 for h=3,5,7\ldots.

DOI Code: 10.1285/i15900932v3n1p149

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