Abstract
A generalized hyperfocused arc 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 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 ( Problem 919), as we point out in the last section.
Keywords: hyperfocused arc; dual 3-net
Original language | English |
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Pages (from-to) | 506-513 |
Number of pages | 8 |
Journal | Journal of Combinatorial Designs |
Volume | 22 |
Issue number | 12 |
DOIs | |
Publication status | Published - 2014 |