TY - BOOK
T1 - Generalized hyperfocused arcs in $PG(2,p)$
AU - Blokhuis, A.
AU - Marino, G.
AU - Mazzocca, F.
PY - 2013
Y1 - 2013
N2 - A {\em generalized hyperfocused arc} $\mathcal H $ in $PG(2,q)$ is an arc of size $k$ with the property that the $k(k-1)/2$ secants can be blocked by a set of $k-1$ points not belonging to the arc. We show that if $q$ is a prime and $\mathcal H$ is a generalized hyperfocused arc of size $k$, then $k=1,2$ or 4. Interestingly, this problem is also related to the (strong) cylinder conjecture [Ball S.: The polynomial method in Galois geometries, in Current research topics in Galois geometry, Chapter 5, Nova Sci. Publ., New York, (2012) 105-130], as we point out in the last section.
AB - A {\em generalized hyperfocused arc} $\mathcal H $ in $PG(2,q)$ is an arc of size $k$ with the property that the $k(k-1)/2$ secants can be blocked by a set of $k-1$ points not belonging to the arc. We show that if $q$ is a prime and $\mathcal H$ is a generalized hyperfocused arc of size $k$, then $k=1,2$ or 4. Interestingly, this problem is also related to the (strong) cylinder conjecture [Ball S.: The polynomial method in Galois geometries, in Current research topics in Galois geometry, Chapter 5, Nova Sci. Publ., New York, (2012) 105-130], as we point out in the last section.
M3 - Report
T3 - arXiv.org
BT - Generalized hyperfocused arcs in $PG(2,p)$
PB - s.n.
ER -