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,thenk = 1, 2, or 4. Interestingly, this problem is also related to the (strong) cylinder conjecture ([2, 5] Problem 919), as we point out in the last section.
Generalized hyperfocused arcs in PG(2,p)
MARINO, Giuseppe;MAZZOCCA, Francesco
2014
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,thenk = 1, 2, or 4. Interestingly, this problem is also related to the (strong) cylinder conjecture ([2, 5] Problem 919), as we point out in the last section.File in questo prodotto:
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