Prefixes of the Fibonacci word that end with a cube
Narad Rampersad
TL;DR
This paper characterizes the positions within the Fibonacci word where prefixes end with a cube, providing an exact description using Walnut, a formal language tool.
Contribution
It offers a precise description of cube-ending prefixes in the Fibonacci word, a novel analysis using Walnut for such combinatorial structures.
Findings
Identifies exact positions of cube endings in Fibonacci word
Uses Walnut to analyze combinatorial properties of Fibonacci prefixes
Provides a formal description of cube-ending prefixes
Abstract
We study the prefixes of the Fibonacci word that end with a cube. Using Walnut we obtain an exact description of the positions of the Fibonacci word at which a cube ends.
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Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · Advanced Mathematical Theories and Applications