On (k,3)-Arcs Derived by Ceva Configurations in PG(2,5)

Abstract

In this study, we investigate complete (k,2)-arcs and (k,3)-arcs derived from a Ceva configuration in the projective plane of order five by implementing an algorithm in C#. Our results indicate the existence of a complete (6,2)-arc that has no points in common with the (7,3)-arc formed by the Ceva configuration. Furthermore, we identify eight different complete (10,3)-arcs that include a Ceva configuration. Additionally, we explore cyclic order Ceva configurations, denoted as C_1,C_2,C_3, and C_4, all of which have a common center. The vertices of each configuration C_i are on the sides of the preceding configuration C_(i-1), with i ranging from 2 to 4. We determine different thirty-two complete (10,3)-arcs and different two complete (6,2)-arcs by constructing cyclic order Ceva configurations C_1,C_2,C_3,C_4 with a common center in PG(2,5).