Generalized Hyperfocused Arcs in math formula

Authors


  • Contract grant sponsor: Seconda Università degli Studi di Napoli; contract grant sponsor: Italian Istituto Nazionale di Alta Matematica; contract grant sponsor: Italian national research project Strutture geometriche, combinatoria e loro applicazioni.

Abstract

A generalized hyperfocused arc math formula in math formula is an arc of size k with the property that the math formula secants can be blocked by a set of math formula points not belonging to the arc. We show that if q is a prime and math formula is a generalized hyperfocused arc of size k, then math formula 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.

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