Symmetries of rhotrix using Aunu permutation pattern

Abstract

This study deals with connection between rhotrices and Aunu permutation patterns. The features of rhotrices and Aunu permutations patterns are observed. A relationship between Aunu permutation patterns and rhotrices is established for a case where n is a prime number equal to 5. It is also observed that the heart of the rhotrix is necessarily 1 everywhere. The derivation of the Aunu permutation pattern from the rhotrix starts from the heart of the rhotrix to the upward direction; from upward direction to the left and to the right of the heart, and finally to the buttom of the heart. When the rhotrix is rotated at right angle, a semigroup is obtained. Embedding an identity element into the semigroup again produces a Carley group.

Keywords: Rhotrices, Aunu permutation patterns, semigroup, carley group, derivation of Aunu permutation patterns.