Circular words and applications
Beno\^it Rittaud (Laboratoire Analyse, G\'eom\'etrie et Applications,, Institut Galil\'ee, Universit\'e Paris-13), Laurent Vivier (Laboratoire de, Didactique Andr\'e Revuz, Universit\'e Paris Diderot)
TL;DR
This paper introduces circular words constrained by Fibonacci-like conditions, explores their structure, and discusses applications in number systems, sequences, and graph theory, while highlighting open questions for future research.
Contribution
It defines Fibonacci-constrained circular words and analyzes their structure, connecting them to various applications and open problems.
Findings
Structural properties of Fibonacci-constrained circular words
Applications to number expansions and sequence properties
Open questions in combinatorics and graph theory
Abstract
We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various situations: periodic expansion of numbers in numeration systems, "gcd-property" of integer sequences, partition of the prefix of the fixed point of the Fibonacci substitution, spanning trees of a wheel. Eventually, we mention some open questions.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Mathematical Dynamics and Fractals