On Third Order Bronze Fibonacci Quaternions

Fibonacci Sequences of Quaternions

In this paper Fibonacci sequences of quaternions are introduced, generalizing Fibonacci sequences over commutative rings, and properties of such sequences are investigated. In particular we are concerned with two kinds of Fibonacci sequences of generalized quaternions over finite fields Fp, with p an odd prime, and their periods.

On The Usual Fibonacci and Generalized Order-k Pell Numbers

In this paper, we give some relations involving the usual Fibonacci and generalized order-k Pell numbers. These relations show that the generalized order-k Pell numbers can be expressed as the summation of the usual Fibonacci numbers. We …nd families of Hessenberg matrices such that the permanents of these matrices are the usual Fibonacci numbers, F2i 1; and their sums. Also extending these mat...

ON THE GENERALIZED ORDER-k FIBONACCI AND LUCAS NUMBERS

In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.

ON QUATERNIONS By

Fibonacci topological order from quantum nets.

We analyze a model of quantum nets and show it has a non-Abelian topological order of doubled-Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined on any lattice, has less complicated interactions, and its excitations are dynamical, not fixed. This Hamiltonian includes terms acting on the spins aroun...