An arc in a projective plane whose secants meet some exterior line
in the minimum number of points is said to be hyperfocused on that
line. This is similar to a concept introduced by Simmons
in the design of a geometric secret sharing scheme. Drake and
Keating have recently rediscovered the idea under the
guise of hyperovals in nets. We will answer two open questions
raised by Drake and Keating. We also provide a classification of
small hyperfocused arcs in Desarguesian planes using the
graph-theoretic concept of 1-factorizations of complete graphs.
Publié le : 2006-01-14
Classification:
hyperovals,
nets,
1-factorizations of complete graphs,
Desarguesian planes,
secret sharing schemes,
51E21,
51A30,
05B25,
05C70
@article{1136902606,
author = {Cherowitzo, William E. and Holder, Leanne D.},
title = {Hyperfocused Arcs},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {12},
number = {5},
year = {2006},
pages = { 685-696},
language = {en},
url = {http://dml.mathdoc.fr/item/1136902606}
}
Cherowitzo, William E.; Holder, Leanne D. Hyperfocused Arcs. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp. 685-696. http://gdmltest.u-ga.fr/item/1136902606/