Exchange of three intervals: itineraries, substitutions and palindromicity
Zuzana Mas\'akov\'a, Edita Pelantov\'a, \v{S}t\v{e}p\'an, Starosta
TL;DR
This paper analyzes three-interval exchange transformations, detailing return times and itineraries, and applies these results to prove a conjecture for infinite words fixed by such transformations.
Contribution
It provides a detailed description of return times and itineraries for three-interval exchanges and confirms a conjecture for infinite words fixed by these transformations.
Findings
Confirmed the Hof-Knill-Simon conjecture for certain infinite words
Described return times and itineraries for three-interval exchanges
Linked interval exchange transformations to properties of fixed words
Abstract
Given a symmetric exchange of three intervals, we provide a detailed description of the return times to a subinterval and the corresponding itineraries. We apply our results to morphisms fixing words coding non-degenerate three interval exchange transformation. This allows us to prove that the conjecture stated by Hof, Knill and Simon is valid for such infinite words.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · Natural Language Processing Techniques