Diagonal function of natural rhotrix

Abstract

Abstract Natural rhotrix refers to the rhotrix whose elements are all natural numbers, arrayed in their natural order. This type of rhotrix has just recently been introduced in literature. Therefore, this work is taking a further look at its properties. It introduces the concept of diagonal function of a natural rhotrix and examines its properties. It is found that the diagonal function of a natural rhotrix is given as . Furthermore, it presents the sum of the other elements outside its diagonals as where is the set of elements along any of its diagonals, , and are the complement of , the index and the heart of respectively. These properties are all peculiar to this beautiful set of rhotrix called the natural rhotrix.