Generating functions of substitutions
Aisling Pouti, Christopher Ramsey, Nicolae Strungaru

TL;DR
This paper establishes a connection between a substitution's aperiodicity and the transcendental nature of its associated generating functions, using recursive structures to analyze roots in specific cases like the Fibonacci substitution.
Contribution
It proves that a substitution is aperiodic if and only if some of its generating functions are transcendental, linking dynamical properties with transcendence.
Findings
A substitution is aperiodic iff some generating functions are transcendental.
Recursive structure of generating functions is used to analyze roots.
Specific analysis conducted for Fibonacci substitution.
Abstract
We prove that a substitution is aperiodic if and only if some of its associated generating functions are transcendental. These generating functions have a recursive structure arising from the substitution which we use to study their roots in the case of the Fibonacci substitution.
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Taxonomy
Topicssemigroups and automata theory · Quasicrystal Structures and Properties · Language, Linguistics, Cultural Analysis
