The Fibonacci–Circulant Sequences and Their Applications

@article{Deveci2017TheFS,
  title={The Fibonacci–Circulant Sequences and Their Applications},
  author={{\"O}m{\"u}r Deveci and Erdal Karaduman and Colin M. Campbell},
  journal={Iranian Journal of Science and Technology, Transactions A: Science},
  year={2017},
  volume={41},
  pages={1033-1038}
}
In this paper, we define the recurrence sequences using the Circulant matrices which are obtained from the characteristic polynomial of the Fibonacci sequence, and then, we give miscellaneous properties of these sequences. In addition, we consider the cyclic groups which are generated by the generating matrices and the auxiliary equations of the defined recurrence sequences, and then, we study the orders of these cyclic groups. Furthermore, we extend the defined sequences to groups. Finally, we… 
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References

SHOWING 1-10 OF 15 REFERENCES
FIBONACCI SEQUENCES IN FINITE GROUPS
The Fibonacci sequence and its related higher-order sequences (tribonacci, quatranacci, /c-nacci) are generally viewed as sequences of integers. In 1960, Wall [4] considered Fibonacci sequences
The Jacobsthal Sequences in Finite Groups
Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k
The Cyclic Groups and the Semigroups via MacWilliams and Chebyshev Matrices
In this paper, we consider the multiplicative orders of the MacWilliams matrix of order $N(M_{N})_{ij}$ and the Chebyshev matrix of order $N(D_{N})_{ij}$ according to modulo $m$ for $N\ge 1$.
Generators and relations for discrete groups
1. Cyclic, Dicyclic and Metacyclic Groups.- 2. Systematic Enumeration of Cosets.- 3. Graphs, Maps and Cayley Diagrams.- 4. Abstract Crystallography.- 5. Hyperbolic Tessellations and Fundamental
VanderLaan Circulant Type Matrices
Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant,
Fibonacci lengths involving the wall number k(n)
Two infinite classes of special finite groups considered (The groupG is special, ifG’ andZ(G) coincide). Using certain sequences of numbers we give explicit formulas for the Fibonacci lenghts of
Truncated Lucas sequence and its period
Fibonacci Length of Generating Pairs in Groups
Let G be a group and let x, y ∈ G. If every element of G can be written as a word $${x^{{\alpha _1}}}{y^{{\alpha _2}}}{x^{{\alpha _3}}} \ldots {x^{{\alpha _{n - 1}}}}{y^{{\alpha _n}}}$$ (1)
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