(2, k)-Distance Fibonacci Polynomials

-̂fibonacci Polynomials

Let MC be the monoid of all Morse code sequences of dots a(:=®) and dashes b(: = -) with respect to concatenation. MC consists of all words in a and b. Let P be the algebra of all polynomials HveMCK ^h r e a l coefficients. We are interested in: a) polynomials in P which we call abstract Fibonacci polynomials. They are defined by the recursion Fn(a, b) = aF^a, b) + bFn_2(a, b) with initial valu...

Some Generalized Fibonacci Polynomials

We introduce polynomial generalizations of the r-Fibonacci, r-Gibonacci, and rLucas sequences which arise in connection with two statistics defined, respectively, on linear, phased, and circular r-mino arrangements.

Generalized Bivariate Fibonacci Polynomials

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...

Bell polynomials and Fibonacci numbers

Nullspace-primes and Fibonacci Polynomials

A nonzero m x n (0, 1)-matrix A is called a nullspace matrix If each entry (/', j) of A has an even number of l's in the set of entries consisting of (/, j) and its rectilinear neighbors. It is called a nullspace matrix since the existence of an m x n nullspace matrix implies the closed neighborhood matrix of the mxn grid graph Is singular over GF(2). By closed neighborhood matrix, we mean the ...