Classification of degree three arcs in PG(2,19) up to stabilizer groups.

Abd-alzahra, Islam A.; Ibrahim, Mohammed A.

An (n, 3)-arc K in projective plane PG(2, q) of size n and degree three is a set of n points such that every line in the plane meet it in less than or equal three points, also the arc K is complete if it is not contained in (n 1,3)-arc. In this paper, the classification of degree three arcs in PG(2,19) is introduced in details according to their stabilizer groups. The motivation for working in the projective plane of order 19 is twofold. First, the size of the largest (n, 3)-arc is not known. Second, the number of (n, 3)-arcs is significantly higher in the projective plane of order 19 than it is in the projective plane of order q for q < 19, giving a large number of (n, 3)-arcs for the study.

EMPLOYEE motivation; POINT set theory; CLASSIFICATION; PROJECTIVE planes

Basrah Journal of Science / Magallat Al-Barat Li-L-ulum, 2024, Vol 42, Issue 2, p146

2664-8288

Academic Journal

10.29072/basjs.20240201