On (k,3)-arcs derived by Ceva configurations in PG(2,5)

Year 2024, Issue: 059, 10 - 18, 31.12.2024

Elif Altıntaş Kahriman , Ayşe Bayar

https://doi.org/10.59313/jsr-a.1559383

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).

Keywords

projective plane, (k,n)-arc, ceva configuration

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