THE RECURRENCE SEQUENCES VIA POLYHEDRAL GROUPS

Year 2018, Volume: 67 Issue: 2, 99 - 115, 01.08.2018

Ömür Deveci Yeşim Aküzüm M. Campbell Colın

Abstract

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

Keywords

Matrix, polyhedral sequences, polyhedral groups, period

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• Current address : Ömür Deveci: Faculty of Science and Letters, Kafkas University 36100, Turkey
• E-mail address : [e-mail] 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 : [e-mail] 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 : [e-mail]