Geodesic
Arcs with large conical subsets
The electronic journal of combinatorics, Tome 17 (2010)

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl EuDML
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\((2,q)\) 
K. Coolsaet; H. Sticker. Arcs with large conical subsets. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/384
@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/}
}
TY  - JOUR
AU  - K. Coolsaet
AU  - H. Sticker
TI  - Arcs with large conical subsets
JO  - The electronic journal of combinatorics
PY  - 2010
VL  - 17
UR  - http://geodesic.mathdoc.fr/articles/10.37236/384/
DO  - 10.37236/384
ID  - 10_37236_384
ER  - 
%0 Journal Article
%A K. Coolsaet
%A H. Sticker
%T Arcs with large conical subsets
%J The electronic journal of combinatorics
%D 2010
%V 17
%U http://geodesic.mathdoc.fr/articles/10.37236/384/
%R 10.37236/384
%F 10_37236_384

Cité par Sources :