Tamás Szőnyi

Small complete arcs in Galois planes

AbstractIn this paper we construct a class of k-arcs in PG(2, q), q=ph, h>1, p≠3 and prove its completeness for h large enough. The main result states that this class contains complete k-arcs with

Covers and blocking sets of classical generalized quadrangles

k \leqslant 2 \cdot q^{{9 \mathord{\left/ {\vphantom {9 {10}}} \right. \kern-\nulldelimiterspace} {10}}} {\text{ }}\left( {10{\text{ divides }}h{\text{ and }}q{\text{ }} \geqslant {\text{ }}q_{\text{0}} } \right).

On q-analogues and stability theorems

Such complete k-arcs are the unique known complete k-arcs with

Note on the structure of semiovals in finite projective planes

k \leqslant {q \mathord{\left/ {\vphantom {q 4}} \right. \kern-\nulldelimiterspace} 4}.

Sets with a large number of nuclei on a conic

In this paper we construct maximal partial spreads in PG(3, q) which are a log q factor larger than the best known lower bound. For n ≥ 5 we also construct maximal partial spreads in PG(n, q) of each size between cnqn − 2 log q and c′ qn − 1.