Complete arcs in inversive planes over prime fields

Concerning maximal arcs and inversive planes

Small Complete Arcs in Projective Planes

In the late 1950’s, B. Segre introduced the fundamental notion of arcs and complete arcs [48, 49]. An arc in a finite projective plane is a set of points with no three on a line and it is complete if cannot be extended without violating this property. Given a projective plane P, determining n(P), the size of its smallest complete arc, has been a major open question in finite geometry for severa...

A class of complete arcs in multiply derived planes

We prove that unital-derived ðq qþ 1Þ-arcs of PGð2; qÞ still yield complete arcs after multiple derivation with respect to disjoint derivation sets on a given line.

New complete 2 - arcs in the uniform projective Hjelmslev planes over chain rings of order 25

In this paper a 2-arc of size 21 in the projective Hjelmslev plane PHG(2,Z25) and a 2-arc of size 22 in PHG(2,F5[X]/(X)) are given. Both arcs are bigger than the 2-arcs previously known in the respective plane. Furthermore, we will give some information on the geometrical structure of the arcs.

Inversive Planes of Even Order

1. Results. An inversive plane is an incidence structure of points and circles satisfying the following axioms: I. Three distinct points are connected by exactly one circle. II. If P, Q are two points and c a circle through P but not Q, then there is exactly one circle c' through P and Q such that cC\c'~ [P]. III. There are at least two circles. Every circle has at least three points. For any p...