The $q$-golden ratio, Catalan numbers, and an identity of Sauermann--Wigderson
Kevin Carde
TL;DR
This paper explores properties of q-Fibonacci numbers, their connection to the q-golden ratio and Catalan numbers, and uses these relationships to prove a combinatorial identity.
Contribution
It introduces new properties of q-Fibonacci numbers and links them to Catalan numbers, providing a novel proof of a combinatorial identity.
Findings
Properties of q-Fibonacci numbers analyzed
Relationship between q-Fibonacci numbers, q-golden ratio, and Catalan numbers established
A new proof of a combinatorial identity provided
Abstract
In this note, we present some basic properties of -Fibonacci numbers and their relationship to the -golden ratio and Catalan numbers. We then use this relationship to give a short proof of a combinatorial identity.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Graph Labeling and Dimension Problems · Advanced Combinatorial Mathematics