Space-filling subsets of a normal rational curve

G. Korchmáros, L. Storme, T. Szonyi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we show that the bisecants of an affinely regular n-gon inscribed in an ellipse of AG(2,q) cover all the points of AG(2,q) except the remaining points of the ellipse and possibly the center of the ellipse, if n≥√2q3/4. This completes the previous investigations of Korchmáros (1993) and Szonyi (1987), who studied hyperbolas and parabolas. The results can be used to construct various complete plane arcs using the method of Segre (1962) and Lombardo-Radice (1956). It is also shown how these results can be used to prove the completeness of particular k-arcs in spaces PG(n,q) of n dimensions that share k - 1 or k - 2 points with a normal rational curve. The best results are obtained by combining algebraic techniques with probabilistic ideas.

Original languageEnglish
Pages (from-to)93-110
Number of pages18
JournalJournal of Statistical Planning and Inference
Volume58
Issue number1
DOIs
Publication statusPublished - Mar 1 1997

Keywords

  • Affine regular polygons
  • Arcs in n dimensions
  • Complete arcs
  • Normal rational curves

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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