Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8)

Khaled Moaz

University of Mosul, department of computer science and mathematics, Mosul, Iraq

Khaledmoaz_m13@gmail.com

Abstract

A k-arc in a plane PG (2, q) is a set of k point such that every line in the plane intersect it in at most two points and there is a line intersect it in exactly two points. A k-arc is complete if there is no k+1-arc containing it. This thesis is concerned with studies a k-arcs, k=4, 5,…., 10 and classification of protectively distinct k-arcs and distinct arcs under collineation. We prove by using computer program that the only complete k-arcs is for, k= 6, 10.

Keywords: k-bracket; Projection; Projective plane; k-arc