A new proof of the existence of \((q^ 2-q+1)\)-arcs in \(PG(2,q^ 2)\) (Q1895160)

The present article contains two theorems and their proofs on existence of \((q^2 - q + 1)\)-arcs in \(\text{PG} (2, q^2)\). The author shows that each point-orbit which is disjoint from the sides of the fundamental triangle is a \((q^2 - q + 1)\)-arc and that each Desarguesian plane of order \(q^2\) contains a cyclic \((q^2 - q + 1)\)-arc.