Abstract Like Fibonacci and Lucas numbers, the Pell family is ubiquitous. Pell and Pell–
Lucas numbers also provide boundless opportunities to experiment, explore, and …

Grover's quantum search and its generalization, quantum amplitude amplification, provide a
quadratic advantage over classical algorithms for a diverse set of tasks but are tricky to use …

Euler's continuants are universal polynomials expressing the numerator and denominator of
a finite continued fraction whose entries are independent variables. We introduce their …

Based on Chebyshov polynomials, one can create an asymmetric cryptosystem that allows
for secure communication. Such a cryptosystem is based on the fact that these polynomials …

We provide a combinatorial proof of the trigonometric identity cos (nθ)= Tn (cosθ), where Tn
is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other …

Abstract The Fibonacci sequence, Lucas numbers and their generalization have many
interesting properties and applications to almost every field. Fibonacci sequence is defined …

The tradition of studies involving the combinatorial approach to recurring numerical
sequences has accumulated a few decades of tradition, and several problems continue to …

In this article we study the index (the largest eigenvalue of the adjacency matrix) in two
special classes of trees, namely: starlike trees and double brooms. For each class, we …

We prove various formulas which express exponential generating functions counting
permutations by the peak number, valley number, double ascent number, and double …

q-Chebyshev polynomials Page 1 1 q-Chebyshev polynomials Johann Cigler Fakultät für
Mathematik, Universität Wien johann.cigler@univie.ac.at Abstract In this overview paper a …