K-regular decomposable incidence structure of maximum degree

Abstract

This paper discusses incidence structures and their rank. The aim of this paper is to prove that there exists a regular decomposable incidence structure J = (P, B) of maximum degree depending on the size of the set and a predetermined rank. Furthermore, an algorithm for construction of this structures is given. In the proof of the main result, the points of the set P are shown by Euler's formula of complex number. Two examples of construction the described incidence structures of maximum degree 6 and maximum degree 30 are given.

Keywords

• regular incidence structure
• partition
• euler's formula of complex number