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 |
|---|---|
| Pages (from-to) | 506-513 |
| Number of pages | 8 |
| Journal | Journal of Combinatorial Designs |
| Volume | 22 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2014 |
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Blokhuis, A., Marino, G., & Mazzocca, F. (2014). Generalized hyperfocused arcs in PG(2,p). Journal of Combinatorial Designs, 22(12), 506-513. https://doi.org/10.1002/jcd.21371