Geodesic
Arcs with large conical subsets
The electronic journal of combinatorics, Tome 17 (2010)
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We classify the arcs in $\mathrm{PG}(2,q)$, $q$ odd, which consist of $(q+3)/2$ points of a conic $C$ and two points not on te conic but external to $C$, or $(q+1)/2$ points of $C$ and two additional points, at least one of which is an internal point of $C$. We prove that for arcs of the latter type, the number of points internal to $C$ can be at most $4$, and we give a complete classification of all arcs that attain this bound. Finally, we list some computer results on extending arcs of both types with further points.
DOI : 10.37236/384
Classification : 51E21, 05B25
Mots-clés : arcs, conics, PG\((2,q)\) 
@article{10_37236_384,
     author = {K. Coolsaet and H. Sticker},
     title = {Arcs with large conical subsets},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/384},
     zbl = {1196.51007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/384/}
}
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K. Coolsaet; H. Sticker. Arcs with large conical subsets. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/384

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