Analysis of the Density of Words under Morphism $\{a,b\}$
Jasem Hamoud, Duaa Abdullah
TL;DR
This paper investigates the density of Fibonacci words and their derivatives through morphism analysis, introducing a novel power operation to compare Fibonacci word densities with other related words.
Contribution
It presents a new power operation for Fibonacci words and compares their densities with other derived words, offering insights into their structural properties.
Findings
Fibonacci word densities are characterized through morphism analysis
A novel power operation is introduced for Fibonacci words
Comparative analysis with other derived words reveals structural differences
Abstract
In this paper, we analyze the density of the Fibonacci word and its derived forms by examining the morphisms associated with each. It offers a comparative analysis of the density of Fibonacci numbers alongside other words derived from Fibonacci word. Fibonacci words over the alphabet , we define a novel \emph{power} operation that yields a formal linear combination in the free abelian group generated by all finite words.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · Advanced Combinatorial Mathematics