The Recurrence Sequences via Polyhedral Groups

Abstract

Abstract. In this paper, we de…ne recurrence sequences by using the relation matrices of the …nite polyhedral groups and then, we obtain some of their properties. Also, we obtain the cyclic groups and the semigroups which are produced by the generating matrices when read modulo and we study the sequences de…ned modulo . Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the sequences de…ned working modulo . Furthermore, we extend these sequences to groups and obtain the periods of the sequences extended in the …nite polyhedral groups case.