THE RECURRENCE SEQUENCES VIA POLYHEDRAL GROUPS

In this paper, we define recurrence sequences by using the relation matrices of the finite 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 a and we study the sequences defined modulo a. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the sequences defined working modulo a. Furthermore, we extend these sequences to groups and obtain the periods of the sequences extended in the finite polyhedral groups case

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  • Current address : Ömür Deveci: Faculty of Science and Letters, Kafkas University 36100, Turkey
  • E-mail address : odeveci36@hotmail.com ORCID: http://orcid.org/0000-0001-5870-5298
  • Current address : Ye¸sim Aküzüm: Faculty of Science and Letters, Kafkas University 36100, Turkey
  • E-mail address : yesim_036@hotmail.com ORCID: http://orcid.org/0000-0001-7168-8429
  • Current address : Colin M. Campbell: School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland E-mail address : cmc@st-andrews.ac.uk