Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomials

TL;DR

This paper explores the relationships between q-analogues of classical combinatorial numbers and polynomials, revealing that q-Catalan numbers, q-central binomial coefficients, and q-Narayana polynomials are moments of certain q-Fibonacci and Lucas polynomials.

Contribution

It establishes new connections between q-analogues of well-known polynomials and moment sequences, expanding understanding of their algebraic and combinatorial properties.

Findings

q-Catalan numbers are moments of q-Fibonacci polynomials

q-Narayana polynomials relate to q-Lucas polynomials

The paper provides new identities linking these q-analogues

Abstract

We show that q-Catalan numbers, q- central binomial coefficients and q- Narayana polynomials are moments of q-analogues of Fibonacci and Lucas polynomials and related polynomials.