REAL

Double blocking sets of size 3q−1 in PG(2,q)

Csajbók, Bence and Héger, Tamás (2019) Double blocking sets of size 3q−1 in PG(2,q). European Journal of Combinatorics, 78. pp. 73-89. ISSN 01956698

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Abstract

The main purpose of this paper is to find double blocking sets in PG(2, q) of size less than3q, in particular whenqis prime. To this end, we study double blocking sets in PG(2, q) of size 3q−1 admitting at least two (q−1)-secants. We derive some structural propertiesof these and show that they cannot have three (q−1)-secants. This yields that one cannotremove six points from a triangle, a double blocking set of size 3q, and add five new pointsso that the resulting set is also a double blocking set. Furthermore, we give constructions ofminimal double blocking sets of size 3q−1 in PG(2, q) for q= 13, 16, 19, 25, 27, 31, 37 and 43. If q >13 is a prime, these are the first examples of double blocking sets of size less than 3q. These results resolve two conjectures of Raymond Hill from 1984.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: Tamás Héger
Date Deposited: 26 Sep 2019 04:01
Last Modified: 03 Apr 2023 06:36
URI: http://real.mtak.hu/id/eprint/101566

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