Dergiler / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2018 / Cilt: 67 - Sayı: 2

THE RECURRENCE SEQUENCES VIA POLYHEDRAL GROUPS

THE RECURRENCE SEQUENCES VIA POLYHEDRAL GROUPS

Yeşim AKÜZÜM, Colin M. CAMPBELL, Ömür DEVECİ

Sayfa
99–115
DOI
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Abstract

In this paper, we de.ne recurrence sequences by using the relationmatrices of the finite polyhedral groups and then, we obtain some of theirproperties. Also, we obtain the cyclic groups and the semigroups which areproduced by the generating matrices when read modulo _ and we study thesequences de.ned modulo _. Then we derive the relationships between theorders of the cyclic groups obtained and the periods of the sequences de.nedworking modulo _. Furthermore, we extend these sequences to groups andobtain the periods of the sequences extended in the .nite polyhedral groupscase.