Farey lines defining Farey diagrams and application to some discrete structures
Daniel Khoshnoudirad · Applicable Analysis and Discrete Mathematics · 2015
The aim of the paper is to study some of the analytical properties of Farey diagrams of order (m,n), which are associated to the (m,n)-cubes, that is the pieces of discrete planes, occurring in discrete mathematics. We give a closed formula for the number of Farey lines defining Farey diagrams. This number asymptotically behaves as mn(m+n)=?(3). Then we establish the relation with some discrete structures in the field of discrete geometry in particular.