Hemisystems of small flock generalized quadrangles

preprint2011arXivOpen access

Abstract

In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order (52,5)(5^2,5) and give numerous further examples of hemisystems in all the known flock generalized quadrangles of order (s2,s)(s^2,s) for s≤11s \le 11. By analysing the computational data, we identify two possible new infinite families of hemisystems in the classical generalized quadrangle H(3,q2)H(3,q^2).

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