BAZI CENTRO-POLYHEDRAL GRUPLARIN PELL UZUNLUKLARI

Yıl 2014, Cilt: 1 Sayı: 1, 81 - 88, 31.12.2014

Ömür Deveci , Hasan Öztürk

Öz

Anahtar Kelimeler

Pell Dizisi , Grup , Uzunluk

BAZI CENTRO-POLYHEDRAL GRUPLARIN PELL UZUNLUKLARI

Öz

In [13], Deveci and Karaduman defined the Pell orbit   of the group   by generated the set  . In this paper, we examined the Pell orbits of the centro-polyhedral groups  ,  ,  ,  ,  ,  ,   for   and the centro-polyhedral groups    ,  ,  ,  ,  ,  ,   with respect to the generating set   and the order   of generators.

Anahtar Kelimeler

Pell Dizisi , Grup , Uzunluk.

Kaynakça

• [1]. H. Aydın and R. Dikici, General Fibonacci sequences in finite groups, The Fibonacci Quart., 36(3) (1998), 216-221.
• [2]. C. M. Campbell, P. P. Campbell, The Fibonacci length of certain centro-polyhedral groups, J. Appl. Math. Comput., 19 (2005), 231-240.
• [3]. C. M. Campbell, H. Doostie and E. F. Robertson, Fibonacci length of generating pairs in groups in Applications of Fibonacci Numbers, Vol. 3 Eds. G. E. Bergum et al. Kluwer Academic Publishers, (1990), 27-35.
• [4]. H. S. M. Coxeter, W. O. J. Moser, Generator and relations for discrete groups, 3 rd edition, Springer, Berlin (1972).
• [5]. P. G. Becker, k-regular power series and Mahler-type functional equations, J. Number Theory, 49(3) (1994), 269-286.
• [6]. W. Bosma and C. Kraaikamp, Metrical theory for optimal continued fractions, J. Number Theory, 34(3) (1990), 251-270.
• [7]. O. Deveci and E. Karaduman, The generalized order-k Lucas sequences in Finite groups, J. Appl. Math., 464580-1-464580-15 (2012).
• [8]. O. Deveci, The k-nacci sequences and the generalized order-k Pell sequences in the semi-direct product of finite cyclic groups, Chiang Mai J. Sci., 40(1) (2013), 89-98.
• [9]. O. Deveci and E. Karaduman, "On the basic k-nacci sequences in finite groups", Discrete Dyn. Nat. Soc., (2011), 639476-1-639476-13.
• [10].O. Deveci and E. Karaduman, The cyclic groups via the Pascal matrices and the generalized Pascal matrices, Linear Algebra and its Appl., 437 (2012), 2538-2545.
• [11]. O. Deveci and E. Karaduman, The Pell sequences in finite groups, Util. Math., to appear.
• [12]. O. Deveci, The Pell-Padovan sequences and the Jacobsthal-Padovan sequences in finite groups, Util. Math., to appear.
• [13]. O. Deveci and E. Karaduman, E., Requrrence Sequence İn Groups, LAMBERT Academic Publishing, Germany, 2013
• [14]. H. Doostie and M. Hashemi, Fibonacci lengths involving the Wall number , J. Appl. Math. Comput. 20 (2006), 171-180.
• [15]. M.S. El Naschie, Deriving the essential fatuares of standard model from the general theory of relarivity, Chaos, Solitons & Fractals, 26 (2005), 1-6.
• [16]. M.S. El Naschie, Stability analysis of two-slit experiment, Chaos, Solitons & Fractals, 24 (2005), 941-946.
• [17]. S. Falcon and A. Plaza, k-Fibonacci sequences modulo m, Chaos, Solitons and Fractals, 41 (2009), 497-504.
• [18]. A.S. Fraenkel and S. T. Klein, Robutst universal complete codes for transmission and compression, Discrete Appl. Math., 64 (1996), 31-55.
• [19]. N.D. Gogin and A.A. Myllari, The Fibonacci-Padovan sequence and MacWilliams transform matrices, Programing and Computer Software, published in Programmirovanie, 33(2) (2007), 74-79.
• [20]. D. Kalman, Generalized Fibonacci numbers by matrix methods, The Fibonacci Quart., 20(1) (1982), 73-76.
• [21]. G. R. Kaluge, Penggunaan Fibonacci dan Josephus problem dalam algoritma enkripsi transposisi+substitusi, Makalah IF 3058 Kriptografi-Sem. II Tahun 2010/2011.
• [22]. E. Kılıç and A.P. Stakhov, On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents, Chaos, Solitons and Fractals, 40 (2009), 2210-2221.
• [23]. B.K. Kirchoof, R. Rutishauser, the phyllotavy of costus (costaceae), Bot Gazette, 151(1) (1990), 88-105.
• [24]. S.W. Knox, Fibonacci sequences in finite groups, The Fibonacci Quart., 30(2) (1992), 116-120.
• [25].K. Lü and J. Wang, k-step Fibonacci sequence modulo m, Util. Math., 71 (2007), 169-178.
• [26]. D. M. Mandelbaum, Synchronization of codes by means of Kautz’s Fibonacci encoding, IEEE Transactions on Information Theory, (1972), 281-285.
• [27]. E. Ozkan, H. Aydin and R. Dikici, 3-step Fibonacci series modulo , Appl. Math. and Compt., 143 (2003), 165-172.
• [28]. R.E.G. Pinch, Recurrent sequences modulo prime Powers, In M. Ganley (ed.) Crptography and Coding III, IMA Conference Series (ns.) vol.45, Inst. Math. And Its Appl., Oxford university Press 1993, Procedings, 3rd IMA, Conference Crptography and Coding, Cirencester December 1991.
• [29]. V.W. Spinadel, The family of metallic means, Vis Math., 1(3) (1999).
• [30]. V.W. Spinadel, The metallic means family and forbidden symmetries, Int. Math. J., 2(3) (2002), 279-288.
• [31]. A.P. Stakhov, A generalization of the Fibonacci -matrix, Rep. Natl. Acad. Sci., Ukraine, 9(1999), 46-49.
• [32]. A.P. Stakhov and B. Rozin, Theory of Binet formulas for Fibonacci and Lucas p-numbers, Chaos, Solitons and Fractals, 27(2006), 1162-1167.
• [33]. W. Syein, Modelling the evolution of Stelar archictecture in Vascular plants, Int. J. Plant Sci., 154(2) (1993), 229-263. [34]. D. Taşçı and E. Kılıç, On the order-k generalized Lucas numbrs, Appl. Math. Comput. 20 (2006), 171-180.
• [35]. N. Tuğlu, E.G. Kocer and A.P. Stakhov, Bivarite Fibonacci like p-polinomials, Appl. Math. and Compt., 155(2004), 637-641.
• [36]. D.D. Wall, Fibonacci series modulo , Amer. Math. Monthly, 67 (1960), 525-532.
• [37]. F. Yilmaz and D. Bozkurt, The generalized order-k Jacobsthal numbers, Int. J. Contemp. Math. Sciences, 4(34) (2009), 1685-1694.