Generalized Hyperfocused Arcs in    P  G  (  2  ,  p  ) | Zendy

Blokhuis Aart | Zendy; Marino Giuseppe | Zendy; Mazzocca Francesco | Zendy

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Generalized Hyperfocused Arcs in P G ( 2 , p )

Author(s) -

Blokhuis Aart,

Marino Giuseppe,

Mazzocca Francesco

Publication year - 2014

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.21371

Subject(s) - mathematics , arc (geometry) , conjecture , combinatorics , prime (order theory) , point (geometry) , section (typography) , property (philosophy) , cylinder , set (abstract data type) , geometry , philosophy , epistemology , computer science , programming language , advertising , business

A generalized hyperfocused arc H in P G ( 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 ([2][S. Ball, 2012], [5][P. J. Cameron, 2008] Problem 919), as we point out in the last section.

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