We define generalized bivariate polynomials, from which specifying initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a matrix approach we derive identities and inequalities that in most cases generalize known results. 1 Antefacts The generalized bivariate Fibonacci polynomial may be defined as Hn(x, y) = xHn−1(x, y) + yHn−2(x, y), H0(x, y) = a0, H1...

In this paper we consider certain generalizations of the well-known Fibonacci and Lucas numbers, the generalized Fibonacci and Lucas p-numbers. We give relationships between the generalized Fibonacci p-numbers, Fp(n), and their sums, Pn i1⁄41F pðiÞ, and the 1-factors of a class of bipartite graphs. Further we determine certain matrices whose permanents generate the Lucas p-numbers and their sum...

In this paper, we …nd families of (0; 1; 1) tridiagonal matrices whose determinants and permanents equal to the negatively subscripted Fibonacci and Lucas numbers. Also we give complex factorizations of these numbers by the …rst and second kinds of Chebyshev polynomials. 1. Introduction The well-known Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 2 Fn+1 = Fn + Fn 1 (1.1...

In this paper, we introduce a new operator defined in give some generating functions of binary products Tribonacci and Lucas polynomials special numbers.

In this paper, an analogue of the Gauss–Lucas theorem for polynomials over algebraic closure [Formula: see text] field text]-adic numbers is considered.

The problem of Hadamard quantum coin measurement in $n$ trials, with arbitrary number repeated consecutive last states is formulated terms Fibonacci sequences for duplicated states, Tribonacci numbers triplicated and $N$-Bonacci $N$-plicated states. probability formulas position are derived Lucas numbers. For generic qubit coin, the expressed by more general, polynomials probabilities. generati...

We study special values of Carlitz’s q-Fibonacci and q-Lucas polynomials Fn(q, t) and Ln(q, t). Brief algebraic and detailed combinatorial treatments are presented, the latter based on the fact that these polynomials are bivariate generating functions for a pair of statistics defined, respectively, on linear and circular domino arrangements.

For a fixed rational point P ∈ E(K) on an elliptic curve, we consider the sequence of values (