Some group actions and Fibonacci numbers

dc.contributor.authorŞanlı, Zeynep
dc.contributor.departmentOthertr_TR
dc.contributor.facultyOthertr_TR
dc.date.accessioned2022-12-26T12:08:50Z
dc.date.available2022-12-26T12:08:50Z
dc.date.issued2022
dc.description.abstractThe Fibonacci sequence has many interesting properties and studied by many mathematicians. The terms of this sequence appear in nature and is connected with combinatorics and other branches of mathematics. In this paper, we investigate the orbit of a special subgroup of the modular group. Taking T c := ( c 2 + c + 1 − c c 2 1 − c ) ∈ Γ 0 ( c 2 ) , c ∈ Z , c ≠ 0 , we determined the orbit { T r c ( ∞ ) : r ∈ N } . Each rational number of this set is the form P r ( c ) / Q r ( c ) , where P r ( c ) and Q r ( c ) are the polynomials in Z [ c ] . It is shown that P r ( 1 ) and Q r ( 1 ) the sum of the coefficients of the polynomials P r ( c ) and Q r ( c ) respectively, are the Fibonacci numbers, where P r ( c ) = r ∑ s = 0 ( 2 r − s s ) c 2 r − 2 s + r ∑ s = 1 ( 2 r − s s − 1 ) c 2 r − 2 s + 1 and Q r ( c ) = r ∑ s = 1 ( 2 r − s s − 1 ) c 2 r − 2 s + 2tr_TR
dc.description.indexTrdizintr_TR
dc.identifier.endpage284tr_TR
dc.identifier.issn/e-issn1303-5991
dc.identifier.issue1tr_TR
dc.identifier.startpage273tr_TR
dc.identifier.urihttps://doi.org/10.31801/cfsuasmas.939096tr_TR
dc.identifier.urihttp://hdl.handle.net/20.500.12575/86481
dc.identifier.volume71tr_TR
dc.language.isoentr_TR
dc.publisherAnkara Üniversitesitr_TR
dc.relation.isversionof10.31801/cfsuasmas.939096tr_TR
dc.relation.journalCommunications, Series A1:Mathematics and Statisticstr_TR
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıtr_TR
dc.subjectSuborbital graphs, Pascal triangle, Fibonacci numberstr_TR
dc.titleSome group actions and Fibonacci numberstr_TR
dc.typeArticletr_TR

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