2013/04/12 by A. Blokhuis, G. Marino, Blokhuis, A. +3
Mathematics · #51E21 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:51E21
paper · pdf · doi:10.48550/arxiv.1304.3617
arxiv created 2013/04/12 · arxiv updated 2013/04/15
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.