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Arcs with large conical subsets

Kris Coolsaet (UGent) and Heide Sticker (UGent)
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Abstract
We classify the arcs in 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.

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Citation

Please use this url to cite or link to this publication:

MLA
Coolsaet, Kris, and Heide Sticker. “Arcs with Large Conical Subsets.” ELECTRONIC JOURNAL OF COMBINATORICS, vol. 17, no. 1, 2010.
APA
Coolsaet, K., & Sticker, H. (2010). Arcs with large conical subsets. ELECTRONIC JOURNAL OF COMBINATORICS, 17(1).
Chicago author-date
Coolsaet, Kris, and Heide Sticker. 2010. “Arcs with Large Conical Subsets.” ELECTRONIC JOURNAL OF COMBINATORICS 17 (1).
Chicago author-date (all authors)
Coolsaet, Kris, and Heide Sticker. 2010. “Arcs with Large Conical Subsets.” ELECTRONIC JOURNAL OF COMBINATORICS 17 (1).
Vancouver
1.
Coolsaet K, Sticker H. Arcs with large conical subsets. ELECTRONIC JOURNAL OF COMBINATORICS. 2010;17(1).
IEEE
[1]
K. Coolsaet and H. Sticker, “Arcs with large conical subsets,” ELECTRONIC JOURNAL OF COMBINATORICS, vol. 17, no. 1, 2010.
@article{1247342,
  abstract     = {{We classify the arcs in 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.}},
  articleno    = {{R112}},
  author       = {{Coolsaet, Kris and Sticker, Heide}},
  issn         = {{1077-8926}},
  journal      = {{ELECTRONIC JOURNAL OF COMBINATORICS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{27}},
  title        = {{Arcs with large conical subsets}},
  volume       = {{17}},
  year         = {{2010}},
}

Web of Science
Times cited: