The complex-type k-Fibonacci sequences and their applications

Deveci Ö; Shannon, AG

The complex-type k-Fibonacci sequences and their applications

Deveci Ö Shannon, AG

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Publisher:: Informa UK Limited
Publication Type:: Journal Article
Citation:: Communications in Algebra, 2020, pp. 1-16
Issue Date:: 2020-01-01

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Field	Value	Language
dc.contributor.author	Deveci Ö
dc.contributor.author	Shannon, AG
dc.date.accessioned	2021-03-05T03:10:46Z
dc.date.available	2021-03-05T03:10:46Z
dc.date.issued	2020-01-01
dc.identifier.citation	Communications in Algebra, 2020, pp. 1-16
dc.identifier.issn	0092-7872
dc.identifier.issn	1532-4125
dc.identifier.uri	http://hdl.handle.net/10453/146807
dc.description.abstract	© 2020 Taylor & Francis Group, LLC. In this article, we define the complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the complex-type k-Fibonacci numbers. Also, we obtain miscellaneous properties of the complex-type k-Fibonacci numbers such as the Binet formulas, the combinatorial, permanental, determinantal representations and the sums. In addition, we study the complex-type k-Fibonacci sequence modulo m and then we give some results concerning the periods and the ranks of the complex-type k-Fibonacci sequences for any k and m which are related the periods of the k-step Fibonacci sequences modulo m. Furthermore, we extend the complex-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the complex-type 2-Fibonacci sequences in the dihedral group (Formula presented.) with respect to the generating pairs (x, y) and (y, x).
dc.language	en
dc.publisher	Informa UK Limited
dc.relation.ispartof	Communications in Algebra
dc.relation.isbasedon	10.1080/00927872.2020.1834573
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0101 Pure Mathematics
dc.subject.classification	General Mathematics
dc.title	The complex-type k-Fibonacci sequences and their applications
dc.type	Journal Article
utslib.for	0101 Pure Mathematics
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	closed_access	*
dc.date.updated	2021-03-05T03:10:44Z
pubs.publication-status	Published

Abstract:

© 2020 Taylor & Francis Group, LLC. In this article, we define the complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the complex-type k-Fibonacci numbers. Also, we obtain miscellaneous properties of the complex-type k-Fibonacci numbers such as the Binet formulas, the combinatorial, permanental, determinantal representations and the sums. In addition, we study the complex-type k-Fibonacci sequence modulo m and then we give some results concerning the periods and the ranks of the complex-type k-Fibonacci sequences for any k and m which are related the periods of the k-step Fibonacci sequences modulo m. Furthermore, we extend the complex-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the complex-type 2-Fibonacci sequences in the dihedral group (Formula presented.) with respect to the generating pairs (x, y) and (y, x).

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http://hdl.handle.net/10453/146807