Related papers: Concatenated Fibonacci and Lucas numbers do not fo…

We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions.…

This paper has been withdrawn by the author due to a crucial error in the definition of homomorphism.

Paper withdrawn - lemma 4.1 was false. Quite a lot of changes need to be made!

In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.

The computer code on which this paper relied contained an error. When corrected, the Monte Carlo evaluation of the ground state occupation is consistent with the conventional grand canonical calculation. Hence, the original version of this…

This paper has been withdrawn by the author due to essential mistakes in some previous versions.

We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the number of Fibonacci compositions to regular compositions where…

This (partly expository) paper originated from the study of Hankel determinants of convolution powers of Catalan numbers and of Narayana polynomials. This led to some Hankel determinants of signed Catalan numbers whose values are multiples…

This submission has been withdrawn by the authors because it is a duplicate of arXiv:hep-ph/0611336. It was due to a technical submission error by the authors.

This paper has been withdrawn by the author, since one of the key results duplicates existing work, as pointed out by a reader. I am currently revising the manuscript.

Submission was withdrawn by authors. arXiv:math/0305140

In this paper, we define the incomplete h(x)-Fibonacci and h(x)-Lucas polynomials, we study recurrence relations and some properties of these polynomials

Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we study the problem of writing repdigits as the difference of two balancing or Lucas-balancing numbers. The method of proof involves the application…

We derive generalizations of a couple of inverse tangent summation identities involving Fibonacci and Lucas numbers. As byproducts we establish many new inverse tangent identities involving the Fibonacci and Lucas numbers.

This paper has been withdrawn due to a crucial theoretical and experimental error.

This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.

This paper has been withdrawn: it has been merged with the preprint to which it refers.

This paper is withdrawn.

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

This paper has been withdrawn by the author due to an error.